







A system of equations. 
20200427 

From solomon: xy + x =28
x + y +4 Answered by Penny Nom. 





A rectangular garde 
20200410 

From Denise: In a rectangular garden a person says "if I made that bed 2 feet wider and 3 feet longer it
Would have been 64 sq,ft bigger. But if it had been 3 feet wider and two feet longer
It would have been 68 sq.ft bigger.
What is the length and width of the garden bed? Answered by Penny Nom. 





A linear system 
20200402 

From Dadzie: x+s=8→1
y+x=13→2
yp=6→3
s+p=8→4 Answered by Penny Nom. 





Simultaneous equations 
20191016 

From deepak: This is too complicated please help me
8/x  10/y = 1 and x+y=9 Answered by Penny Nom. 





Can one equation with two variables be solved algebraically? 
20190830 

From Don: Can one equation with two variables be solved algebraically? Answered by Penny Nom. 





Two linear equations with a fraction 
20190426 

From Asha: 2x=3y …1
x2+4/3(y+1) ...2
note: … is equation Answered by Harley Weston. 





Simultaneous equations with fractions 
20181214 

From zaheer: solve simultaneous equations and give answer in fractional form
3x  2 = 4y +5/3
y + 7 = 2x + 4
would really appreciate some help on this please Answered by Penny Nom. 





Are those two equations the same? 
20180605 

From Francisco: Solve for y: 2(x+3)=y x=5
Solve for y: (x+3)2=y x=5
Are those two equations the same? Answered by Penny Nom. 





Simultaneous equations with fractions 
20170909 

From Farah: Hi, my name is Farah. I hope you can help me with this question . X/2 + g/5= 3 and 2g  f = 10 Answered by Penny Nom. 





Simultaneous equations 
20170902 

From keto: xy=2,x^2+xy=12 Answered by Penny Nom. 





Simultaneous equations with fractions 
20170602 

From Jamal: 1/x + 1/y =5 and 1/y  1/x =1 Answered by Penny Nom. 





Algebra 
20170528 

From Kerim: I need to solve this equation.
y=at^2  2at
x =2a√t
Express y in terms of x and a
Give in the form y=(x^p/ma^3)  (x^q/na) where p,q,m and n are integers Answered by Penny Nom. 





Five equations 
20170116 

From Muhammed: A x 4 = E
B ÷ 4 = E
C + 4 = E
D  4 = E
___________
& A + B + C + D = 100
what is the value of E Answered by Penny Nom. 





Simultaneous equations with fractions 
20161221 

From Kimi: I am stuck on this,can someone please help me????
1/2x+1/3y=11
8x+2/5y=102
Can someone please explain how to solve questions like these??
Or else I will never learn...
Thank you Answered by Penny Nom. 





Simultaneous equations 
20161125 

From Rohan: x2/3 + y  1/4 = 13/12
2x/2 + 3 + y/3 = 11/6 Answered by Penny Nom. 





Two equations 
20160917 

From Nilesh: How to solve (xy)^1/2 + 3(xy) = 30 ; xy + 3(xy) = 11? Answered by Penny Nom. 





The temperature inside and outside a greenhouse 
20160722 

From Mehzad: Every day, the temperature in a greenhouse is at its low temperature, 70 degrees Fahrenheit, at 2 a.m. and at its high temperature, 84 degrees Fahrenheit, at 2pm. Its temperature increases linearly between 2 am and 2pm , and decreases linearly from 2 pm and to 2am. The outside temperature follows the same linear patterns, but has a low temperature of 60 degrees Fahrenheit at 2 am and a high temperature of 78 degrees Fahrenheit at 2 pm. At which of the following times will the temperature inside and outside the greenhouse be the same?
a) 8:00 am
b) 12:00 noon
c) 4:00 pm
d) The two temperatures will never be the same Answered by Penny Nom. 





Two equations with fractions 
20160722 

From kanesh: p/2+q/3=3
p/4+2q/3=3 Answered by Penny Nom. 





Simultaneous equations 
20160625 

From sena: 2x/3+3y/2=1
4x5y=22
simultaneous equation Answered by Penny Nom. 





The difference between the ares of two rectangles 
20160609 

From Ingrid: I am trying to help my son with an area question.
I have the answer, from the solutions, but I cannot figure out how to teach him.
Question:
Two rectangles have lengths 13cm and 19cm respectively.
Their total area is 376cm squared.
If both their widths are whole numbers, what is the difference in their areas?
I know that this is solvable once I determine the widths of the rectangles ,
but how do I go about finding that?
Thanks for your help Answered by Chris Fisher and Harley Weston. 





A pair of equations with fractions 
20160511 

From tiya: hello, i want to know how to solve this question.
m/6+2n/3=6
m/10=2n/5=2 Answered by Penny Nom. 





Solve for x and y 
20160227 

From ntshidi: Y=1/2x+4and1/4x6 Answered by Penny Nom. 





Two equations in two unknowns 
20160213 

From Anumba: 4x + 2y = 4
7x  y = 11 Answered by Penny Nom. 





A system of linear equations 
20160124 

From kareem: my name is kareem
and i am a student i have a math puzzle and i tried to solved it but it always have same mistake
xy=9
x+z=12
zn=14
y+n=2 Answered by Penny Nom. 





Two transport companies 
20160106 

From Brynleigh: The Sugar Sweet Company will choose from two companies to transport its sugar
to market. The first company charges $5096 to rent trucks plus an additional fee of
$200.75 for each ton of sugar. The second company charges $5500
to rent trucks plus an additional fee of $175.50 for each ton of sugar.
For what amount of sugar do the two companies charge the same?
What is the cost when the two companies charge the same? Answered by Penny Nom. 





Constructing simultaneous linear equations 
20151228 

From Deborah: Linda thinks of a twodigit number. The sum of the digits is 8. If she reverses the digits, the new number is 36 greater than her original number. What was Linda's original number?
Thank you! Answered by Penny Nom. 





Linear equations in two variables 
20151213 

From priya: I have problem in solving these equations please help me today itself very urgent:
I)2x+y=y
II)pie*x+y=9 Answered by Penny Nom. 





Four equations in 3 unknowns 
20150823 

From damien: solve:
S x U  T = 44
T  U x S = 36
U + T  S = 7
U x U / S = 4 Answered by Penny Nom. 





The method of elimination 
20150501 

From oreanna:
Question from oreanna, a student:
How do u solve 2x+9y=3
7x4y=25 in elimination Answered by Penny Nom. 





A word problem with fractions 
20150409 

From Lorraine: If the numerator of a certain fraction is doubled and the denominator is increased by 1, the fraction becomes 1/2.
If the numerator of the original faction is squared and the denominator is decreased by 2, the fraction becomes equal to 1.
Let x be the numerator and let y be the denominator of the original fraction.
Write down two simultaneous equation in x and y.
Solve these equations to find two possible values for the given fraction. Answered by Penny Nom. 





Two equations with fractions 
20150226 

From Pulane: Hi math centre I've been trying to solve these equations for days now please help
(6/x)(1/y)=4
(9/x)+1=(2/y)
Please help me solve them simultaneously
Thank you Answered by Penny Nom. 





Two equations 
20150216 

From nigel: 2x+1/2y=1
6x3/2y=21 Answered by Penny Nom. 





1999 equations in 1999 unknowns 
20141128 

From Subrahmanya: Solve the following system of 1999 equations in 1999 unknowns :
x1+x2+x3=0, x2+x3+x4=0……., x1997+x1998+x1999=0,
x1998+x1999+x1=0, x1999+x1+x2=0.
(in x1,x2,...................,x1999 the numbers 1,2,.............,1999 are subscripts) Answered by Penny Nom. 





Two quadratic equations 
20141120 

From rajesh: Sir,
I would like to discuss on question
Find the value of variable X and Y, equations are
X2+Y2+2XY=25
X2+Y22XY=1
Sir, my point is equation looks not so easy.My opinion is there many
(more than 4)value possible for both X and Y.
Kindly help me.
Waiting for your response.
regards,
rajesh Answered by Penny Nom. 





A linear system 
20141014 

From pheter: 4/x  1/y = 3 .... equation (1)
6/x  2/y = 5 .... equation (2) Answered by Penny Nom. 





Two equations in x and y 
20140925 

From seyilogo: solve y=2x  3 and (4x  2y) / x + y = 1 simultaneously Answered by Harley Weston. 





Two equations in two variables 
20140918 

From Susan: (28x + 36y)  [20000  .75(28x + 36y) + 60000] = 5000
x + y = 10000
solving two equations involving variables Answered by Penny Nom. 





The method of elimination 
20140705 

From leo: please explain how can i solve this problem
3x6y=38
6x9y=44
using elimination and simultaneous method thank you :) Answered by Penny Nom. 





Simultaneous equations 
20140620 

From rana: solve the simultaneous equations
a)3x=7y
12y=5x1 Answered by Penny Nom. 





Simultaneous equations with fractions 
20140419 

From Maryam: I looked at your example of simultaneous equations with fractions and applied it to my question from an educate exam papers but I couldn't get it to work. The question is:
x/8  y = 5/2
3x + y/3 = 13 Answered by Penny Nom. 





Simultaneous fractional equations 
20140215 

From benjamin: hi math central. benjamin here. during class, i had problem with this topic. normally i wont have problems with math but this topic i just too hard for me. please help i am having exam and test next week on this topic
here is the question:
using substitution method, solve the simultaneous equation.
(x+1)/(y+2)=0.5
(x2)/(y1)=1/3 Answered by Penny Nom. 





Two nonlinear equations 
20140126 

From Naryn: (1÷x) + (1÷y) = (7÷12)
xy = 12 Answered by Penny Nom. 





A linear equation 
20131226 

From khushboo: A farmer sowed wheat and paddy in two fields of total area 5000 sq.m. Write a linear equation and draw a graph to represent the same? Answered by Penny Nom. 





Substitution type simultaneous equations 
20131103 

From Kayla: I am having problems with substitution type simultaneous equations, when the variable you are substituting is a algebraic one:
y=x^23x+4 and 3x2y=1
I have rearranged 3x2y=1 to get x=(1+2y)/3 but when I substitute this x value into the other equation, I get the wrong answers!
Would appreciate any help! Thank you. Answered by Penny Nom. 





A system of equations 
20130813 

From Nina: 3x2y=8
x+3y=5
What is the solution of the system of equations Answered by Penny Nom. 





Four equations 
20130808 

From may: HI how to solve this 4 equations?
A+C = 0
4A+B8C+D=1
3A+16C8D=29
12A+3B+16D=5 Answered by Robert Dawson. 





Simultaneous equations 
20130710 

From Warren: solve this simultaneous equation: xy=4
2x+3y=14 Answered by Penny Nom. 





4 linear equations with 3 unknowns 
20130412 

From Marian: how to solve for 3 unknowns in 4 simultaneous equations Answered by Penny Nom. 





Simultaneous equations with fractions 
20130331 

From Terence: 5/x6/y=1
17/x+30/y=16
I been spending whole day to solve this question. Would be very grateful if you can help I try
The denominator value is a equations term which make is simultaneous equations so hard. Answered by Penny Nom. 





f(x) + f ''''(x)=0 
20130305 

From Andreea: Hei. I don’t speak lot of english but here is my question,hope u understand: f(x) + f ````(x)=0. so, my question. what is f(x), where f ````(x) is f(x) derivative by four time ? i tried to find the answer and i knew f(x) is something like that f(x)=e^x*sinx but miss something. Answered by Brennan Yaremko. 





A word problem involving toys 
20130214 

From sandy: Each boy gets 5 toys.Each girl gets 3 toys.There are 150 pupils.
The boys had 74 more toys than girls.
How many boys?
How many girls? Answered by Penny Nom. 





Dropping supplies from an airplane 
20130214 

From Claire: An airplane flying at an altitude of 3500 feet is dropping supplies to researchers on an island. The path of the plane is parallel to the ground at the time the supplies are released and the plane is traveling at a speed of 300 mph.
a) write the parametric equations that represent the path of the supplies
c)How long will it take for the supplies to reach the ground?
d) how far will the supplies travel horizontally before they land? Answered by Penny Nom. 





Simultaneous equations 
20130210 

From Michael: 2P + 1/3V =8
3P  2/V=5 Answered by Penny Nom. 





Two quadratic equations 
20121122 

From fahmie: graph and solve the intersection of the following equations:
x^2+y^2=4
x^2+2y=4 Answered by Penny Nom. 





A word problem involving a fraction 
20121012 

From Derrick: If the numerator and denominator of a fraction are both decreased by 1 the fraction becomes 2/3. If the numerator and denominator are both increased by 1 the fraction will be 3/4. Find the original fraction. How to do? Answered by Penny Nom. 





2x+underroot2=3x43underroot2 
20120709 

From Eshraj: 2x+underroot2=3x43underroot2 Answered by Penny Nom. 





Parametric equations 2 
20120225 

From Kathy: If the angle at time 0 is not 45 degrees how can you find the initial velocity? Ball thrown from height of 7 feet. Caught by receiver at height of 4 feet after traveling 90 feet down the field. Find initial velocity. You had a similar problem answered but the angle was 45 degrees so the cos and sin were equal and the equations were simpler to work with. Thank you! Answered by Harley Weston. 





Linear equations 
20111006 

From Hannah: I am confused about a question on my homework, here is an example on what I need to do:
You own a sightseeing boat tour. Kids' admission costs $5, adults' admission costs $8.
During that day you get (madeup number) $521 with 71 admissions.
How many of each passenger boarded?
I tried something like
5x + 8y = 521
x + y = 71
But, I still don't understand how to solve it! Help? Answered by Penny Nom. 





A picture with a frame 
20110819 

From Aniish: A picture 8inches by 12inches is placed in a frame of uniform width. If the area of the frame equals the area of the picture find the width of the frame? Answered by Penny Nom. 





A linear equation with fractions 
20110713 

From Simon: I would like to ask if you would be able to explain : linear equation: 2 1/2 (X1)  x+3 /3 = 4 , the first step shows multiplying by 2 then multiplying by 3. etc. What I don't understand is where the 2 in multiplying by 2 comes from? ( the three is pretty obvious being x+3 /3 (to get rid of the divided by) ) .
Thanks for your help. Answered by Penny Nom. 





U(n+1) = 2Un + 1 
20110522 

From Cillian: In a certain sequence, to get from one term to the other you multiply by 2 and add 1, i.e. This is a difference equation of form: U(n+1) = 2Un + 1. prove that there is a maximum of 2 perfect squares in this sequence Answered by Claude Tardif. 





Eliminate y 
20110407 

From Lynn: 2x + y = 8
y + 3z =5
z + 2w =1
5w + 3x = 9
Form three equations with y eliminated Answered by Penny Nom. 





Tony and his friends 
20110321 

From Mieke: Using the following statements and the information given, how much money did each friend have.
Mike says, "I have $41.00 more than Tony."
Jessica says, "I have 6 times as much as Tony plus $2.00."
Ashley says, "I have 13 times the amount Tony has."
Sara says, "I have the 8 times the amount Tony has."
The total together they had was $304.00 Answered by Penny Nom. 





Simultaneous equations 
20101205 

From ryan:
Question from ryan, a student:
3 4
   = 1 (1)
x y
7 2 11
   =  (2)
x y 12 Answered by Chris Fisher and Stephen La Rocque. 





What is the speed of each car? 
20101104 

From Jennifer: two cars are 420 miles apart and traveling towards each other along the same road. They meet in 3.5 hours. One car is traveling 15mph slower than the other. What is the speed of each car?
This must be solved using a system of equation, I have no idea? Answered by Stephen La Rocque. 





Algebraic Equations 
20100810 

From Justin: the amount of money that Mika has if she has some quarters
how fast Rya runs if she runs 5 mi/h slower than Danae
please help,
thanks, justin Answered by Robert Dawson. 





Four less than three times a number is 14 
20100416 

From David: My daughter has two questions that we could use some help with.
First ?
Four less than three times a number is 14
Secound?
The quotient of 15 and w Answered by Penny Nom. 





A system of equations 
20100330 

From samantha: the equations of two lines are 6xy=4 and y=4x +2.what is the value of x in the solution for this system of equations? Answered by Penny Nom. 





The sides of a 306090 triangle 
20100329 

From maris: Find the sides of a 306090 triangle whose perimeter is 6. The solution must use systems of equations using 3 variables. Answered by Penny Nom. 





How many CDs and videos did the store sell? 
20100301 

From dawn: A used book store started selling CDs and videos. In the first week,the store sold 40 used CDs and videos,at 4.00
per CD and 6.00 per video.The sales for both CDs and videos totaled 180.00 she wrote a system of equations to represent the situation.Then she graph the system of equations
thanks Dawn Answered by Tyler Wood. 





Substitution 
20100214 

From Izayah: what is 3 ways to find the meeting point of y=2x+4 and 3x+y=7
by making 2 table and using a graph Answered by Stephen La Rocque. 





A piece of string 8 inches long is cut in two pieces 
20100202 

From Susan: If you have a piece of string 8 inches long and cut it in two pieces. Then take the pieces and forms
each into a square such that the area of each squares added together equals 2. How long are the
sides of the squares?
Susan Answered by Penny Nom. 





A pair of simultaneous equations 
20100109 

From Yumiko: Solve the following pair of simultaneous equations.
x^2 4x = y^24
3y=2x  3 Answered by Penny Nom. 





Solving two equations, one with a square root 
20091123 

From kacie: y = square root of x+3
x4y = 7
im having trouble with this problem...i have to find where they intersect. Answered by Harley Weston. 





541.39(1 + i)^15 = 784.09 
20091014 

From Fitore: Hi, I noticed that this question was already posted up, however I was hoping I could solve it without having to use logs. Can you please help me? The equation is:
541.39(1 + i)^15 = 784.09 Answered by Penny Nom. 





A right triangle 
20091012 

From Josseph: A right triangle has an area of 84ft sq. and a hypotenuse 25ft long. What are the lengths of the other two sides? Answered by Penny Nom. 





Two equations in two unknowns 
20090918 

From Citizen: x+3y=7
x+4y=7 Answered by Penny Nom. 





The method of substitution 
20090917 

From laura: ok! i really need help with this question plz help!!
x=  4y +5
x+2y = 7 Answered by Penny Nom. 





Quadratic equations 
20090830 

From jovian: how can i find the quadratic equation of the roots 2/5 and 1/3? Answered by Stephen La Rocque. 





Simultaneous equations 
20090828 

From onias: solve 3/a  2/b = 1/2 , 5/a + 3/b = 29/12 Answered by Robert Dawson. 





y=2x+1 and y=2x1 
20090828 

From MARICELA: Need help of how to work this problems
y=2x+1 and y=2x1
First of all what is the difference?
Second I think is easy just to work with the X y with the line in the middle
but how do you get the numbers for each side. Answered by Penny Nom. 





Linear equations 
20090823 

From shwetha: The length of a rectangle is greater than the breadth by 18 cm. If both length and breadth are increased by 6 cm then area increases by 168 cm square. Find the length and breadth of the rectangle. Answered by Stephen La Rocque. 





Two equations 
20090531 

From tony: y = 1.2x  32.7,
y = 0.7x + 46.15
can you please solve this for me? i am not able to figure it out... thank you
tony Answered by Penny Nom. 





Two equations 
20090518 

From Bob: solve the system:
x/2  2y= 8
3x + 2/3y= 10 Answered by Stephen La Rocque. 





Stairway construction 
20090502 

From Olivia: Hi, I'm Olivia and I'm in 8th grade studying algebra 1. I'm having some trouble with my math project. It has to do with rules of stairway construction. It says that there are two generally accepted rules to building stairs.
Rule 1: x+y=43 and x+y=46 (cm)
Rule 2: 2y+x=61 and 2y+x=64 (y is the riser and x is the tread length)
I cant figure out how to graph them...it says they're supposed to intersect to make a square which is like the safety zone for building stairs (the stairs' rise and tread lengths are plotted as points) any points outside of that square are considered unsafe.
Did i explain it ok? Thanks for your help.
olivia Answered by Penny Nom. 





Negative nine minus 7x = negative 5 
20090423 

From gigi: what is negative nine minus 7x = negative 5 Answered by Robert Dawson. 





An infinite number of solutions 
20090324 

From Sean: this is a linear equations problem;
first:
3535.5 + Fbd (.866) + Fbc (.5)  Fab (.5) = 0
and
3535.5  Fab (.866)  Fbc (.5)  Fbd (.5) = 0 Answered by Harley Weston. 





The substitution method 
20090218 

From Nicolette: I am working on linear programming problems that I need to solve pairs of linear equations for. I am confused and am not sure how to solve these problems!
5x+3y=7 y=x3 How can i solve this using the substitution method? Answered by Penny Nom. 





A rectangular park 
20090206 

From Debbie: A park named Writer's Rectangle opened in town. When asked about the dimensions of the rectangle, the city planner, responded with these clues: The diagonals of the rectangular park plus its longer sides together measure seven times one of the shorter sides. The length of one diagonal is 250 m longer than one of the shorter sides. Use this information to find the area of the park. Answered by Stephen La Rocque. 





The substitution method 
20090206 

From amber: Pleasse help me with this problem
x+y=2
y2x=1 Answered by Penny Nom. 





Simultaneous equations with an xy term 
20090201 

From angelee: xy+5x2y10=0
2x+y=1 Answered by Penny Nom. 





Sheep, goats, and hogs 
20090123 

From La: A man buys sheep, goats, and hogs, to the number of 100, for 100 crowns; the sheep cost him 1/2 a crown apiece; the goats cost him 11/3 crowns apiece; and the hogs cost him 31/2 crowns apiece. How many had he of each? Answered by Robert Dawson. 





System of equations  comparison method 
20090102 

From nick: Hi, I am doing a project on system of equations by using comparison method,
but for some reason or another, i can't seem to find any information on the
comparison method at all. So, please would you help me by giving me a website
that you know of that has some information on my method. And, if you know the
answer, can you please tell me why or when do we use system of equations by
using comparison method?
Thank You Answered by Robert Dawson. 





Quadratic equations arising from practical problems 
20081124 

From Lenval: Why do quadratic equations arising from practical problems often give physically impossible solutions such as negative distances, negative times or, say, a polygon with a negative number of sides? For example: "A river in flood carries a tree tsquared  23t metres downstream in t seconds. How long does it take for the tree to be carried 50 metres downstream?" This gives t=25 and t=2. Please explain the second 'solution', which is not physically possible. Answered by Chris Fisher and Victoria West. 





Separating variables 
20081104 

From Terry: by separating variables solve the initial value problem
(x+1)y' + y = 0 y(0) = 1 Answered by Harley Weston. 





A linear system 
20081022 

From Tiffany: solve:
x + y + z = 4
2x  3y  z = 1
4x + y  2z = 16 Answered by Penny Nom. 





Two equations in two unknowns 
20081017 

From Dushayne: Please help me in solving this problem:
a. 3x4y=32
5x+2y=10
b. 2x+3y=11
4x+3y=10 Answered by Penny Nom. 





Two equations in two unknowns 
20080801 

From James: Question from james, a student:
3x+2y=9;24x2y=18
My math teacher says that it is (2,4)
Can someone please explain how to figure this out by graphing? Answered by Victoria West. 





Simultaneous equations 
20080723 

From Franco: Solve
3 D + E  F = 10
2 D  F = 4
3 D  4 E  F = 25
Franco Answered by Penny Nom. 





solving four simultaneous equations 
20080718 

From Muhammad: 2B2C+4E=1
A+B+C+D=0
2B2C2D+E=0
B+C+4D2E=0 Answered by Janice Cotcher. 





3y^2  48 = 0 
20080623 

From marquis: 3y^2  48 = 0 Answered by Stephen La Rocque. 





Cows and chickens 
20080616 

From damebochie: I got this problem and want to write a system of equation for it:
Farmer Joe has cows and chickens on his farm. One day he count 76 legs and 24 heads. How many cows and how many chickens are on the farm? write a system of equations and solve.
I don't have any problem to solve it, but I just can;t see how I am going to write this system of equation.
Thank you so much for helping? Answered by Harley Weston. 





Substitution method 
20080530 

From taquicia: 2yx=3
x=5+y Answered by Janice Cotcher. 





Polar coordinates 
20080305 

From kumi: 2.Sketch the graph of r=(2)/(1sinθ). Make sure you show a complete chart demonstrating how you arrive at your sketch, and sketch the graph neatly and clearly with proper labeling.
b. change the equation above to cartesian coordinates and identify the type of graph.
c.explain which coordinate system gives an easier function to graph and why
d.find a function of the form r=f(θ) for a circle centered at (8,π/2) and with the point (0,0) lying on the circle Answered by Penny Nom. 





Parametric equations 
20080305 

From kumi: I have made a picture of a football pass 45 degrees with 30yds and height of 7ft and 4ft. But I am just stuck there. I have stared at the worksheet for soo long. I have no idea how to solve this, and I don't even know where this is going (I don't understand how parametric equations work). Can you help me with this problem?
1.The quarterback of a football team releases a pass at a height, h, of 7ft above the playing field, and the football is caught by a reciever at a height of 4ft, 30yds directly downfield. The pass is released at an angle of 45 degrees with the horizontal with an initial velocity of vo. The parametric equations for the position of the football at time t are given, in general, by x(t)=(vo cosθ)t and y=h+(vo sinθ)t16t^2.
a. find the initial velocity of the football when it is released
b. write the specific set of parametric equations for the path of the football
c.use a graphing calculator to graph the path of the football and approximate its maximum height
d. find the time the reciever has to position himself after the quarterback releases the football Answered by Harley Weston. 





Simultaneous equations 
20080229 

From CONOR: I was wondering if you could help me with this problem
7x  5y = 1
3y = 4x Answered by Penny Nom. 





Two job offers 
20080210 

From Kelly: Raja has been offered two jobs.
Each of these jobs takes 24 weeks to complete.
One job pays $3440 every 8 weeks. The other job pays $2700 every 6 weeks.
Raja wants to accept the job that pays more per week.
Show how to use equations to help Raja make her choice. Answered by Penny Nom. 





Two equations in x and y 
20080201 

From leslie: 6x+8y=40 4x+5y=25 Answered by Penny Nom. 





18/95 x t =3 3/5 
20080128 

From emily: 18/95 x t =3 3/5 Answered by Penny Nom. 





x=sint, y=cos2t 
20080114 

From Art: How do i transform x=sint y=cos2t into a function in terms of x and y Answered by Harley Weston. 





System of equations 
20071206 

From Jenn: change the equation,xy=4 to form y=mx+b
the solution to the system of equations y=2x and y=x+3 is Answered by Stephen La Rocque. 





Chicken and goat feet 
20071205 

From Kim: Old McDonald raises goats and chickens. The animals have a total of
100 heads adn 360 feet. How many goats and how many chickens does Mr.
McDonald have? Answered by Stephen La Rocque and Penny Nom. 





A particle moves in the xyplane 
20071112 

From Russell: A particle moves in the xyplane with
X = 2t^3  12t^2 + 18t
Y = 3t^4  28t^3 + 72t^2
find an equation of the line tangent to the given curve at t_0_ = 1
note: t_0_ is t subscript 0 Answered by Harley Weston. 





a/5= b/7= 8/3 
20071027 

From Kristine: how do you solve for a and b in this equation:
a/5= b/7= 8/3 Answered by Penny Nom. 





4x+8y=32 
20071018 

From Sara: Rewrite the following equation:
4x+8y=32
in function form ("solve for y"). Answered by Penny Nom. 





Four triangles in a square 
20071015 

From Kristina: A square with side lengths of 6 cm is divided into 3 right triangles and a larger isosceles triangle. If the three right triangles have equal area, find the exact area of the isosceles triangle. Answered by Stephen La Rocque. 





Substitution method 
20071011 

From Kevin: 3xx+2y=36y=11 Answered by Stephen La Rocque. 





Coin jar 
20071007 

From a student: Sally empties his jar of coins. It contains $3.75 in nickels, dimes, and
quarters. The number of dimes is twice the number of nickels and the number
of quarters is three less than the number of nickels. Determine how many nickels,
dimes, and quarters were in the in the jar. Answered by Stephen La Rocque. 





Solving four simultaneous equations (system of four linear equations) 
20071007 

From Johan: I need some help in solving this question
x + 2y  3z + 4w = 12
2x + 2y  2z + 3w = 10
0 + y + z + 0 = 1
x  y + z  2w = 4 Answered by Stephen La Rocque. 





Problems solved using quadratic equations 
20071007 

From Lisa: a. Two positive numbers differ by 5. Their product is 234. What are the two numbers?
b. The sum of two numbers is 12. Their product is 30. What are the two numbers?
c.Two numbers differ by 5. Their squares differ by 55. What are the two numbers?
d. The sum of two numbers is 15. Their product is 56. By forming an equation, find the two numbers. Answered by Penny Nom. 





Finding equations, intersection point of two lines at right angles 
20070922 

From Yaz: Find the equation of the line joining A(1,9) to B(6,120). Another line passes through C(7,5) and meets AB at rigth angle of D. Find the euation of CD and calculate the coordinates of D. Answered by Stephen La Rocque. 





Two equations in two unknowns 
20070914 

From CAMEILA: NEED T0 SOLVE THIS EQUATION
Y = 2X + 6
Y + 6 = 2x Answered by Stephen La Rocque. 





Parametric equations 
20070822 

From will: Graph and make a sketch of x = ysquared  6y + 11 in parametric mode (hint: you need to come up with 2 parametric equations).
i have already figured out that the cartesian form of the parametrics will be y = +/ sqroot(x2) + 3, but i do not know how to produce 2 parametric equations from this. Answered by Penny Nom. 





What feature on a graph shows the solution? 
20070819 

From San: To solve the equation 2sinx+square root 3=0, what feature of the graph,
in the form y=asinx+b would show the solution? Draw a graph to show
the solution. thanks. Answered by Stephen La Rocque. 





Finding the radius of an inscribed circle 
20070705 

From Maria: I need to find the radius of a circle which is inscribed inside an obtuse triangle ABC. I know all the angles and all the lengths of the triangle. Answered by Stephen La Rocque and Chris Fisher. 





Simultaneous equations : the Elimination method 
20070621 

From Patricia: I need to find the value of X and Y using the Elimination method.
5/x + 3/y=4
25/x2/y=3 Answered by Stephen La Rocque. 





Angles of depression 
20070613 

From Phonda: The pilot of a small private plane can look forward and see the control tower for a small airstrip. Beyond that is a large factory that is 3 milies from the airstrip. The angles of depression are 12.5 degrees and 4.8 degrees respectively.
Find the airplane's altitude, to the nearest ten feet. Answered by Stephen La Rocque. 





What happens when you have zero's on both sides? 
20070605 

From Lily: On the substitution method what happens when you have zero's on both
sides of the equation? Is that considered no solution or infinitely many? Answered by Stephen La Rocque and Penny Nom. 





System of equations 
20070524 

From Chris: Find all real solutions (x,y,z,w) of the system of equations:
2y= x + x/17, 2z= y + y/17, 2w = z + z/17, 2x= w + w/17 Answered by Penny Nom. 





Set up two simultaneous equations 
20070521 

From Admire: The cost of producing windscreen wipers blades at a factory ais partly fixed (due to operating overheads) and partly dependent on the number of blades produced. It costs $300 to produce 1000, and $600 to produce 5000 blades. How much would it cost to produce 24000 blades? Answered by Penny Nom. 





A tugboat's speed 
20070430 

From Amanda: a tugboat must travel 24 miles against a 4 mile per hour current on the Potomac River and return. At what
constant speed must the tugboat travel to make the trip in 12 hours. Round answer to the nearest tenth mph. Answered by Stephen La Rocque. 





Two equations 
20070429 

From lavon: I'm having trouble figuring out a linear equation, can you help?
 3x + 2y = 8
3x + 2y = 8 Answered by Penny Nom. 





Simultaneous equations 
20070416 

From kyrie: simultaneous equation
4x + 3y = 21
2x * y = 8 Answered by Penny Nom. 





Solve for x and y 
20070327 

From anthony: solve y=4x and x+y=5 Answered by Sara Ulmer. 





Simultaneous equations with fractions 
20070228 

From Alyca: Hello Math Central, I am a grade 10 student taking Academic math. Our unit right now is method of substitution and elimination. I'm stuck on this one question that I've been doing forever. Please help =)
*For this equation I have to do method of elimination, but it's so much harder with fractions...could some one please explain to me how to do it step by step?* x y 2    =   3 6 3 x y 1    = 1 12 4 2
Answered by Steve La Rocque and Ashley Mang. 





Simultaneous equations with envelopes 
20070208 

From Mick: There were 17 envelopes bought, some were brown, some were white. The brown envelopes cost one cent more per envelope than the white ones. The total cost was 80 cents. How much of each type of envelope was bought? Many thanks! Answered by Stephen La Rocque. 





Dividing money unequally 
20070206 

From Linda: I have a total of $13,826.48. It is to be divided by 15 kids  2 of the kids only get half of what the other 13 do  how much do the 13 get and how much does the 2 get? Thanks Answered by Haley Ess and Steve La Rocque. 





Equations with fractions 
20070206 

From Juan and Derek: 3/4x=1/2 3/4+1/5x+1/3=4/5x Answered by Penny Nom. 





Nickels, dimes and quarters 
20070205 

From Avinash: Mary has 48 coins made up of nickels, dimes and quarters with a total value of $5.10. She has 4 more dimes than nickels and quarters combined. How many coins of each kind does she have? Use matrix to solve the system Answered by Stephen La Rocque. 





Fencing a field 
20070201 

From Carol: "The area of a rectangular field is 1200m^2. Two parallel sides are fenced with aluminum at $20/m. The remaining two sides are fenced with steel at $10/m. The total cost of the fencing is $2200." What is the length of each side fenced with aluminum and steel? Answered by Stephen La Rocque. 





The substitution method 
20070131 

From Victoria: how do i solve this problem using the substitution method? 2x5= 14 7x+14y= 5 Answered by Stephen La Rocque. 





The elimination method 
20070131 

From Addrianna: x2y=2 3x5y=7 Answered by Stephen La Rocque. 





A boat travels 60 miles downstream in the same time it takes to go 36 miles upstream 
20070127 

From Liz: A boat travels 60 miles downstream in the same time it takes to go 36 miles upstream. The speed of the boat in still water is 15 mi/h greater than the speed of the current. Find the speed of the current. Answered by Stephen La Rocque. 





The sum of the digits of a twodigit number is 13. 
20070127 

From Liz: The sum of the digits of a twodigit number is 13. If the digits are reversed, the new number is 9 more than the original number. Find the original number. Answered by Penny Nom. 





An algebra exercise 
20070124 

From Clara: Given x + 2y = 2 and x  2y = 18, find: a) x^2  4y^2 b) x^2 + 4y^2 Answered by Stephen La Rocque and Penny Nom. 





Points of intersection 
20070118 

From Mark: Find the points of intersection of the given pair of curves. 2x  3y = 8 and 3x  5y = 13 Answered by Steve La Rocque and Haley Ess. 





A system of equations 
20061113 

From Katrina: solve the system of equations using either the substitution or the elimination method. 2x3y= 12 and 4x+6y=15 Answered by Penny Nom. 





(4x5)^2 = 32 
20061111 

From Tracey: (4x5)^2 = 32 Answered by Stephen La Rocque and Penny Nom. 





Simultaneous equations 
20061106 

From An other: e^2yx+2=0 ln(x+3)2y1=0 Answered by Penny Nom. 





Balancing equations 
20061026 

From Della:
With the following equations, how do you know whether you need to apply the multiplication or division rule of equality? 75% t = 18 120% w = 72 Answered by Penny Nom. 





Word equations 
20061022 

From Samira: One half of a number is subtracted from the sum of onethird and onequarter of the same number. If the result is 16, find the number. Answered by Stephen La Rocque. 





How much did I spend on the first trip? 
20060910 

From Alexander: I have $600 to spend.
I take 10 shopping trips.
Each trip I spend $10 more than the last trip.
How much did I spend on the first trip?
Answered by Stephen La Rocque. 





Making and using equations 
20060830 

From Brooke:
write an equation to model the relationship between these variables. Define the variables you use, and refer to your notes for a variety of formats of equations we have studied this year.
week 1: 3 birds infected
week 2: 15 birds infected
week 3: 75 birds infected
week 4: 375 birds infected
Answered by Stephen La Rocque. 





If 5x + 4y = 6 then x + y = ? 
20060818 

From Vijai: If 5x+4y=6
then x+y=? Answered by Stephen La Rocque and Penny Nom. 





I want to calibrate a glucose meter 
20060727 

From John: If I have 3 glucose control solutions having:
Low  50 mg/dl
Normal  100 mg/dl
High  330 mg/dl
I want to calibrate a glucose meter but I need more than these 3 data points. How can I mix these up to get different concentrations in between 50 and 100, 100 and 330. I would like to mix up different concentrations and put them in test tubes or whatever to do some calibration work. Like 70 mg/dl, 90 mg/dl, etc. More data points should be in between say 50 and 100 since this is normal, 90 mg/dl is considered close to normal.
Answered by Stephen La Rocque. 





Three people go to a store where there is a sale 
20060530 

From Geocee: Three people go to a store where there is a sale. One person buys two shirts, one pair of pants and one sweater. The second person buys one shirt, two pairs of pants and two sweaters. The third person buys three shirts and four pairs of pants. Find the price of each item if the first person spent $155 and the second and third person spent $235 each. Answered by Stephen La Rocque. 





Simultaneous Equations 
20060524 

From Angie:
Question: solve the equations
2x3yz=0
3x2y+z=5
x+3y2z=14
for x,y,z
Answered by Stephen La Rocque. 





x7=20 and 2x+5=17 
20060404 

From Janette: I'm trying to help out my daughter, it has been much too long since I've been in school. The question is x7=20 and the other question is 2x+5=17. What are the formulas? Answered by Penny Nom. 





2x+5y=3 And x+3y=7 
20060403 

From Lloyd: simplify 2x+5y=3 And x+3y=7
Answered by Penny Nom. 





2x+3y=0 and 3xy=0 
20060314 

From Lisa: my name is lisa I am doing math for work and i have a math problem to solve and i need help with it here is the question 2x+3y=0 and 3xy=0 this is one question can you help me please Answered by Penny Nom. 





One boundary of a pond is parabolic in shape. 
20060120 

From Glenn: One boundary of a pond is parabolic in shape. The boundary passes through the points A(20,45), B(40,40) and E(30,35). The equation of the parabola is of the form y=ax2+bx+c. Find the equation of the parabola and the coordinates of the vertex of the parabola. Any assistance you could provide would be greatly appreciated. Answered by Penny Nom. 





Simultaneous Equations 
20051221 

From Matt: I have these two equations,
336 = 60a + 10b
and
432 = 84a + 6b
Am I right in saying both a and b are 4.8? Answered by Penny Nom. 





5(x3)/4 =x+1 
20051214 

From Jennifer:
I have two problems i am stumped on I don't know how to help my daughter.
5(x3)/4 =x+1
3(x+12)/5 =x +2
Answered by Penny Nom. 





An integer equation 
20051201 

From Henry: 3x = 2y + 7
I know the answer: x=9 and y=10, but what are the algebraic steps to solve the equation? Answered by Penny Nom. 





Graphing two lines 
20051120 

From A student: About y = 5x + 24 and y = 3x  8
1. Graph both equations on the same set of axes. When you made your graph, how did you choose the range of x and y values?
2.Find the point of intersection for the graphs.
3. Test the point of intersection you found by substituting its coordinates into the equations. Do the coordinates fit the equations exactly? Answered by Penny Nom. 





Solving a pair of equations 
20051110 

From Steven: what is answer to
2 x + y = 1
y = ^{1}/_{3} x  4 Answered by Penny Nom. 





3x  5  (4x  8) = 2(2  3x) + 29 
20051106 

From Emma: I do not get how to "solve for x". For example:
3x  5  (4x  8) = 2(2  3x) + 29 Answered by Penny Nom. 





Simultaneous equations 
20051013 

From Daniel: 5x + 3y = 22
4x  7y = 20 Answered by Penny Nom. 





6x+7=8x13 
20050927 

From A student: show me how to do 6x+7=8x13 Answered by Penny Nom. 





14p  8 = 22 + 20p 
20050927 

From Tiffany: 14p  8 = 22 + 20p Answered by Penny Nom. 





A system of equations 
20050902 

From Gina: How do you interpret the solution of a system of equations by the corresponding graph? Demonstrate your answer by the use of an example. Answered by Penny Nom. 





Discriminant 
20050620 

From A student: If a quadratic has real root, its discriminant b24ac>=0 Is there any similar condition or method by which you can find whether roots of a cubic equation are real or not? Answered by Chris Fisher. 





y = x+2 and y = 2x  1 
20050503 

From Kimberley: Question:
y=x+2
y=2x1 Answered by Penny Nom. 





2^10 = 1/2^x  1 
20041213 

From Randy: Could you explain to me how the following equation is solved please.
2^10 = 1/2^x  1 Answered by Harley Weston. 





The substitution method 
20041128 

From A student: I Was working and i ran into this problem can you help me solve it using the substitution method?
3x2y=10
x+5y=27 Answered by Penny Nom. 





Solve for a and t 
20041023 

From Justin: How do I solve for "a" and "t" in the equations:
1000t= 4000 + 2000t + (1/2)at^2
1000=2000 + at Answered by Penny Nom. 





The integrating factor method 
20040805 

From A student: Whilst using the integrating factor method, I am required to integrate a function multipled by another function.
say f(t) = exp(kt) and some other function g(t); where exp = exponential and k is some constant.
Integral f(t)*g(t) dt or
Integral exp(kt)*g(t) dt
What would the result of this integral be? I have never met an integral like this before. Would it simply be exp(kt)*g(t)/k?
More specifically, the problem and my attempted answer is in PDF format:
In my attempted solution, I am unsure about the last two lines I have written out, as it relates to integrating a function multipled by another function. Answered by Harley Weston. 





Solving some quadratic equations 
20040715 

From A student: Could you please solve the following for x
x^{2}+6=5x
x^{2}+16=8x
2x+21=3x^{2} Answered by Penny Nom. 





Setting up an equation 
20040430 

From Matt: I am trying to determine the dimensions of a 22 megapixel digital camera chip that has a 3:2 ratio. We know then, that: 3x = 2y (or 1.5x = y)
and that
xy = 22
Beyond this, I don't know how to hook those 2 seemingly unrelated facts together. Answered by Penny Nom. 





The substitution method 
20040214 

From Keisha: I need to solve this problem by using the substitution method.
3x+y=1
x=2y+5
Please help me understand the method to solve. Answered by Penny Nom. 





Diamonds and Pearls 
20031211 

From Lauren: A crown holds a total of 3080 jewels.
It is made up of diamonds and pearls.
There are 10 times as many diamonds as there are pearls.
How many pearls are there? Answered by Penny Nom. 





Mr.Carter is very cautious 
20031126 

From Bob: Mr.Carter is very cautious. He decides to invest in only three stocks: one low stock, one high stock, one medium stock. Given that the expected annual yields are 6% for low stock, 7% for medium stock, and 8% for high stock, he wants his investment in medium stock to be half of his total investment in low and high stock. How much should I invest in each type fo stocks to expect a total annual return fo $650 form my investments? Answered by Harley Weston. 





Systems of equations 
20031119 

From Scott: I hope that u can help me....I
am a college student taking a class in Pre Calculus.....I have homework
due this Friday and it counts a BIG Percentage on my FINAL grade.....I
am getting mixed up and can not figure out a few problems.....Please help
me.....
Method Of Subsitution
Problem 1. y 8x = 5
x(squared) + y(squared) = 25
Problem 2. y = x(squared)  2x  6
Y = x(squared)  4
Answered by Penny Nom. 





The product of the page numbers 
20031107 

From Morgan and Mom: You open a book and the product of the page numbers is 12,656. What are your page numbers? Answered by Penny Nom. 





Solve for x 
20031027 

From Lonnie: i need help with solving equations and formulas such as 3x+b=6x, for x. I do not understand how you find x. Answered by Penny Nom. 





Substitution method 
20030914 

From John:
Hello, my name is john and while I was finishing up my work I stumbled into these problems. a/4b=1 a+b=11 and 6ab=5 4a3b=8 Thanks a lot. I really need some help :) John Answered by Penny Nom. 





Two equations 
20030821 

From Jennifer:
The following problems have me stuck and any help would be greatly appreciated seeing my text book is doing me no favours:
3^{2a+1}  283^{a} + 9=0 and 5^{2m}  5^{m}=20 Answered by Penny Nom. 





x+3 = 15x 
20030719 

From Nathan: Without the use of trial and error, is there a way of solving for x where x + 3 = 15x? I know that x = 0.1875, but how do I find whether x + 3 is positive or not if I did not have this information (In other words, how would I solve whether the xvalue was 3 or less, or if it was more than 3)? Answered by Claude Tardif and Penny Nom. 





Setting up a word problem 
20030630 

From Christie: A rectangular corral is forty feet longer than it is wide. If the perimeter is 220 feet, determine the length and width of the corral. Answered by Penny Nom. 





Sesame Street on Stage 
20030625 

From Christie: Sesame Street on Stage has different ticket prices for adults and for children under 6. Beth and her two children, ages 3 and 4, paid $15 to gain entrance, while Jamie and John Jacobs and their 2year old daughter got in for $19.50. What is the ticket price for adults? Answered by Penny Nom. 





The substitution method 
20030414 

From Patty:
I need help with the following: 5x  4y = 13 2y + 3x = 1 Answered by Penny Nom. 





(n+17)(n+7) = 0 
20030305 

From Janea:
What is the answer to 1. (n+17)(n+7)=0 What is the answer to:2. (y15)(y100)=0 Answered by Penny Nom. 





Two equations in two unknowns 
20030206 

From Patrick: What are all ordered pairs of real numbers (x, y) for which: y^{x2  7x + 12} = 1 and x + y = 6? Answered by Penny Nom. 





Quadratic equations 
20021210 

From Katie: just bugging the hell outta me and I cannot figure it out for the life of me.
1)x2x1 =0 Find both roots. You must simplify both of your roots. This equation requires the use of the Quadratic Formula. I have tried everything for this and I am still either getting the wrong answers, and end up getting really frustrated. If you could find the answers and tell me how you did it I would greatly appreciate it! Then the second problem is
2) The square of a certain negative number is equal to 70 decreased by 3 times the number. Find the answer! On this one I set it up but still came out with the wrong answer. So if you could help me on this one I would greatly appreciate it! Answered by Penny Nom. 





The substitution method 
20021115 

From A student: Solve by using the substitution method. x = 3y  1 x + 2y = 9 Answered by Penny Nom. 





Determining a parabola 
20021106 

From Shelley: let (0,3) and (1,9)and (1,1) be given points in a parablola. Determine a b and c Answered by Penny Nom. 





How many trees were planted in March? 
20021020 

From Allison: The number of trees planted by the Alpine Nursery in April was 3 more than twice the number of trees planted in March. If 71 trees were planted in april, write and solve an equation to find how many trees were planted in March. Answered by Penny Nom. 





Solving an equation 
20020922 

From Emanuel: how do u solve these problems?:
30/x=7+ 18/2x
3m+1/4 = 2 32m/3 Answered by Penny Nom. 





Formulating equtions 
20020914 

From Theresa: Hello. In math class we have to formulate equations for certin questions for extra credit. We are allowed to ask anyone and anyone can do it for us and explain it to us. Could you please do that? Here are the questions  Jordan has 3 times as much money as Reva. Together they have $44. How much money does each have?
 The Tigers played 48 games. They won twice as many as they lost. How many did they win?
 There are 900 students in Sewickley Academy. There are 20 more girls than boys. How many girls are there?
 A board 400 cm long is cut into 2 pieces. One piece is 66 cm longer than the other. Find the lenght of the shorter piece.
Answered by Penny Nom. 





A solution to an equation 
20020828 

From A student: How do you determine whether a pair of numbers is a solution for an equation? If you could identify the specifics steps I need to take to determine whether it is a solution or not would be appreciated! Thanks i.e. x4=0 Pairs of numbers as possible solutions (4,7) (3,4) (0,4). Answered by Penny Nom. 





Express 5120 as a sum of consecutive numbers 
20020825 

From Todd: Express 5120 as a sum of more than 1 consecutive number. Answered by Leeanne Boehm. 





Two equations 
20020726 

From Derek: 1. 3x + 2y = 4 2. 7x + 2y = 24 finding x and y. Answered by Penny Nom. 





25m = 100 
20020422 

From Megan: If 25m = 100, Then m equals what number? Answered by Penny Nom. 





An augmented matrix 
20020420 

From A student: Hi my math teacher asked us to solve an augmented matrix. I am in twelfth grade and need help. The book we are working on is college algebra. Here it is a+2b+c=0 2a+5b+4c=1 ab9c=5 Answered by Penny Nom. 





Pairs of equations 
20020404 

From A student:
high school level student is asking
y=4x x=4y
x+y=5 3x+2y=20
y=x1 3xy=4
x+y=3 2x3y=9
x+5y=4
3x+15y=1
. . .
Answered by Penny Nom. 





The substitution method 
20020224 

From Joe: whats the answer to this question? 3x+y=11 x+2y=3 its substitution method i am having alot of trouble figuring it out. send the answer as soon as possible. thank you Answered by Penny Nom. 





Algebra review questions 
20020114 

From A student:
 A wildebeast was observed racing a distance of 86.4m in 4.8 seconds. Find the speed of the wildebeast in m/s.
 8x  7  5x = 23
 7 z  3 (z + 2) = 26
Answered by Penny Nom. 





Simultaneous equations 
20011217 

From Matthew: 4x + y = 4 2x  3y = 5 what is x and y Answered by Penny Nom. 





A rightangled triangle 
20011213 

From Pamela, Jeff, Kayleigh and Jacob: A rightangled triangle has one side that is 8 cm shorter that the hypotenuse. The other side is 1 cm shorter than the hypotenuse. Find the length of the sides. Answered by Penny nom. 





Two equations in two unknowns 
20011204 

From Courtney: y = 3x + 2 y = 4x  5
solve for x Answered by Penny Nom. 





Undetermined coefficients 
20011122 

From Hoda: The equation is: y"  2y' + y = t e^{t} + 4 We need to use The method of Undetermined coefficients. I have tried assuming that the solution is Ate^{t}+Be^{t}+C, but all I get is C=4 and I tried (At^{2}+Bt+C)e^{t}+D, but again I get 0=0 when I calculate the first and second derivatives, so i get no information on the constants. Any suggestions? Answered by Harley Weston. 





Investing in a yacht 
20010926 

From Junior: Marvin and his four friends wish to invest in a yacht by sharing equally in the cost. As the date of sale approaches, Marvin realizes that if three more people join the partnership, each partner's share would decrease by $18,000. How much does the yacht cost? Answered by Penny Nom. 





Solving trig equations 
20010922 

From Asad: Can you please explain to me how to solve trig Equations,e.g sin(x)=x^{4}+12/2+cos(x)=x^{6}+9/3= (if this can be solved) Answered by Claude Tardif. 





Matrix reconstruction 
20010719 

From Guy: Is there a way to get the sums of rows, columns and diagonals of an n x n matrix to reconstruct the original matrix? Answered by Walter Whiteley and Patrick Maidorn. 





Common solution 
20010602 

From Samantha:
 Solve for common solution: x+y=6 2x3y=2
 Solve for y in terms of x: 3xy=4
Answered by Penny Nom. 





Graphing equations 
20010501 

From A student: If, for example, 4x^{2}12x+9=0 and 4x^{2}+12x9=0, which I'm assuming it does since you can derive that equation from the first, why do those two equations have different graphs? Answered by Penny Nom. 





Solving some equations 
20010416 

From Justin: Solve the following equations for x  x+7=10
x=
 x7=10
x=
 3x=7
x=
 x/3=10
x=
 .
 .
 .
 .
Answered by Penny Nom. 





Where do the lines y=2x4 and y=x1 intesect? 
20010406 

From Bryce: solve the following problem by setting them equal to each other. Solve for x and y. Where do the lines y=2x4 and y=x1 intesect? Answered by Penny Nom. 





Systems of equations 
20010316 

From joy: How do u solve problems using systems of equations? ~ finding x and y~ ex:
26 = 3x  2y 42 = 4x + y Answered by Penny Nom. 





Quadratic equations 
20010311 

From Philip: I am a student in the UK and i am in secondary school and i am doing my GCSE next year. here are my questions: solve the following equations correct to 2 decimal each time. [1] 2xsquared + 5x = 1 [2] 3xsquared(2x+1)=1 [3] xsquared + 7x + 2 = 2x + 4 [4] 5xsquared  3x = xsquared + 4 Answered by Penny Nom. 





The substitution method 
20010305 

From A student: Solve each system of equations by the substitution method. Show your work.  y = 8
7x = 1  y
 y = x  1
4x  y = 19 Answered by Penny Nom. 





Solve for the variable 
20010228 

From Ashley: I've got 2 questions. We (my dad and I) can not figure them out. please help me.  21 = 9  2 (4a + 2) and I am supposed to find out what the variable is.
 2/3 n + 3/8 n = 15/16 (those are fractions). Again, I need to find out what the variable is.
Answered by Penny Nom. 





Solving Equations 
20010223 

From Stephanie: Do you know who came up with solving equations? Do you have any websites that can give me good information on solving equations? Do you know any history on solving equations? Do you know what solving equations is used for? And finally............Sorry about all of the questions :) Has the form of solving equations changed from the time it came out to now? Answered by Juci McDonald. 





Linear equations 
20010213 

From Jamie: I have a question how do you do linear equation? Answered by Penny Nom. 





Blood flow and age 
20010111 

From Gayle: I don't understand the second part of this problem Here is the first part that was correct. A 35yr old has 100% blood flow. A 65yr old has 64% blood flow. Find the rate of change per yr in the percent of blood flow. (This part is correct) m=(64100)/(3565)= 36/30= 1.2 per year of blood flow. Now, here is the second part I DON'T UNDERSTAND! .Let b represent the percent of blood flow and a represent a person's age. Write an equation that you could use to predict the percent of blood flow for a person of any age over 35. Answered by Penny Nom. 





x^5 + y^5 + z^5 = w^5 
20010111 

From Samuel Brown: x^{5} + y^{5} + z^{5} = w^{5} I have no idea whether or not this is possible. Answered by Claude Tardif. 





A piecewise linear equation 
20001124 

From Jacky: There is a light bulb and it is given that the light bulb cost $0.75 and the cost of operating it is $0.0081 per hour. From the information give, I came up with the linear equation: Let c be total cost and Let h be hours used. Therefore: c = 0.0081h + 0.75 represents the total cost of the light bulb and the electricity. However, the second part of the question added the fact that the light bulb will only last for 800 hours. If the light bulb is replaced as soon as it burns out exactly after every 800 hours, how can I write an equation that represents that? Is it possible? What would it look like on the graph. Answered by Harley Weston. 





Connecting to a water line 
20001020 

From Vanja: My question is...A house is to be connected to a new water main that runs along the line y=2/3x1. The connection point at the house has coordinates (2,9), where the units represent metres. What lenght of plastic pipe is needed to connect to the water main at the closest point? Answered by Penny Nom. 





2step equations 
20001011 

From Jen: i don't get how you find the answer to these equations 140= 4 12e x/2 + 6 = 4 Answered by Penny Nom. 





Buying art supplies 
20000918 

From Travis: An art teacher buys exactly 100 items at this sale, and the total cost before tax is $100. She buys at least one of each item. How many of each item does she buy? Markers $0.50 Sketch Pads $3.00 Paint Sets $10.00 Answered by Denis Hanson. 





Two linear equations 
20000914 

From David Dean: 2a + 1b = 3.39 3a + 3b = 6.59 What formula do I use to find what a = ? Answered by Harley Weston. 





Two linear systems 
20000801 

From A student: please help me with this homework question. 5/x + 6/y= 19/6 3/x + 4/y =2 hint: let a = 1/x and b = 1/y substitute these expressions into the system to find a and b. Then find x and y. This is a question I answered wrong on a test: solve the given system for x, y, and z. Express your solutions in terms of a, b, and c. Answered by Penny Nom. 





n! = 42(n2)! 
20000721 

From Damon Bailey: Solve n! = 42(n2)! Answered by Paul Betts. 





The equation of a parabola 
20000522 

From Ian Forsyth: Given the points A(0,0) B(60,10) C(24,d) find the equation of the parabola. leave the equation in terms of x, y and d if the general form of a quadratic is y = ax^{2} + bx + c. Answered by Penny Nom. 





A matrix equation 
20000514 

From A student: Right now, we are dealing with matrices and we are supposed to solve the following problem on our graphingcalculators: 2a+3b4c+d=20 a2b+3c5d=14 3a+4b2c+3d=19 5ab+6c+4d=5 Answered by Penny Nom. 





Taxis in Chicago 
20000327 

From A high school studenthigh school student: Suppose that taxis pick up and deliver passengers in Chicago, which is divided into three zones. Records kept by the drivers show that of the passengers picked up in Zone 1, 50% are taken to a destination in Zone 1, 40% to Zone 2, and 10% to Zone 3. OF the passengers picked up in Zone 2, 40% go to Zone 1, 30% to Zone 2, and 30% to Zone 3. Of the passengers picked up in Zone 3, 20% go to Zone 1, 60% to Zone 2 and 20% to Zone 3. Suppose that at the beginning of the day, 600 of the taxis are in Zone 1, 100 in Zone 2, and 300 in Zone 3. What is the distribution of taxis in the various zones after all have had two riders? Answered by Harley Weston. 





A system of equations in five unknowns 
20000320 

From Will: I have been having some problem with the following question for some time. I would appreciate any help on solving the problem or a solution. Q: Assume that a system of equations in the unknowns x1, x2, x3, x4 and x5 when converted to row echelon form gives . . . Answered by Penny Nom. 





Simultaneous equations 
20000311 

From Laura Molck: My name is Laura Molck and I am in Year 11 in Australia. Please help me with the following. I know that they are all simultaneous equations which I can do but I have trouble with the formulae to work the equations. Can you please help!! 1. A tent manufacturer produces 2 models, Outback and Bushwalker. From earlier sales records it is known that 20% more of the Outback model is sold than the Bushwalker. A profit of $200 is made on each Outback sold, but $350 is made on each Bushwalker. If during the next year a profit of $177,000 is planned how many of each model must be sold? Answered by Penny Nom. 





Systems of linear equations 
20000310 

From Ann Marie Devereux: hi there!!, I guess I have a problem!!! 3x+4y=10 (over) 4x+y=9 2x=5y+3 (over) x=3y+1 Answered by Penny Nom. 





Some equations 
20000308 

From Maria: Hi, could you help me with these questions: Find x & solve  72x/3=9
 4x+3/5=2
 62x=14
 1/7x=4/3+1/6
Answered by Penny Nom. 





A mixture problem 
20000306 

From Rebecca Edwards: A tank in which cholocate milk is being mixed contains a mixture of 460 liters of milk and 40 liters of chocolate syrup initially. Syrup and milk are then added to the tank at the rate of 2 liters per minute of syrup and 8 liters of milk per minute. Simultaneously the mixture is withdrawn at the rate of 10 liters per minute. Find the function giving the amount of syrup in the tank at time t. Answered by Harley Weston. 





Midpoints and endpoints 
20000215 

From Jessica Sipes: I need to know how to find and endpoint using the midpoint and the other endpoint. Answered by Penny Nom. 





Quadratic 
20000126 

From Karen Johnson: What is the reasoning behind the title quadratic equation? Answered by Penny Nom. 





Ax + By = C 
20000118 

From Fatiha Khanboubi: I was wondering if you could please explain to me how I would write the equation of line through the given points [(4,1), (6,3)] in Ax+By=C form. Answered by Harley Weston. 





Parallel lines 
20000112 

From Lori: Find an equation of the line parallel to the given line containing the given point. x + y = 2; (1,2) We know parallel line have the same slope and we know the answer y = x + 3. Answered by Penny Nom. 





Solve for v 
19991209 

From Beth: 13/4(v+2)=5 Answered by Penny Nom. 





Systems of equations 
19991206 

From Roger Hornbaker: I am having problem figuring out x and y solutions.  5x + y = 4
3x  y = 4  3x + 2y = 6
 3x + y = 0 Answered by Penny Nom. 





The elimination method 
19991202 

From Jennifer: Could I get an answer to this one: 2x+5y=36 3x+2y=32 I have to use the Elimination method, as I already know how to do Substitution. How do I begin and show my work? I'm attempting to eliminate the values for y. Answered by Penny Nom. 





How wide is the well? 
19991124 

From Chris Baranski: There is a well and in the well there are 2 sticks one is 2 meters long the other is 3 meters long and they are opposite to each other. They are leaning against the wall of the well. The place where they touch is 1 meter of the bottom of the well. How wide is the well? Answered by Chris Fisher. 





Linear models 
19991109 

From Helen Moreno: What is a linear model? Answered by Harley Weston. 





Multiple step problems 
19991109 

From Maria Rainsdon: I don't understand how to solve these multiple step problems. I wasn't there when my teacher explained it and I am really lost. Here is one of the probs I don't understand: 3m+6=m6. Answered by Penny Nom. 





Equations with fractions 
19991010 

From Lori: I'm a secondary student. How would you figure out a problem such as t2/t =14/3t  1/3. The book gave one example but it is really easy. The work YOU have to do is totally different. You don't have to tell me the answer just how to do such problems like these. Answered by Penny Nom. 





Why is slope designated m? 
19990818 

From Peter Komlos: Why is the slope of a line is designated by the letter "m"? Answered by Penny Nom. 





Parametric Equations 
19990806 

From Nicholas Lawton: Show that an equation of the normal to the curve with parametric equations x=ct y=c/t t not equal to 0, at the point (cp, c/p) is : yc/p=xp^2cp^3 Answered by Harley Weston. 





Graphing a linear equation 
19990527 

From Dylan Bradley: Im in Grade ten and am doing linear equations, I cann't figure out how to make a chart for questions like y = 2x + 3 Answered by Penny Nom. 





Question about 3rd degree polynomials 
19990423 

From Patrick Bryan: What is the general solution to the equation with the form: a*x^3 + b*x^2 + c*x + d = 0 I have once seen a solution to this a few years ago, but I do not recall if it was a general solution. What I do know, is that you could simplify this equation to: a*x'^3 + p*x' + q = 0... Answered by Doug Farenick. 





Parallel and perpendicular lines 
19990423 

From Crystal Pilling: My name is Crystal Pilling and I am in 9th grade algebra. We are currently studying parallel and perpendicular lines. I am having trouble with this problem: 3/4x  5y= 16, (5,6) I have to find a line that is perpindicular to this line on a graph. HELP ME PLEASE!!!!! Answered by Penny Nom. 





Shopping at Wegman's 
19990422 

From Stan: Joanne, Steve, Pat, Alice, Joan, and Bill go to Wegman's at the same time. Joanne buys 2 gal of milk, 1 dozen oranges, 8 apples, and 2 lb. of ground beef, paying a total of $13.24. Steve buys 3 qts. of milk, 5 lbs. of ground beef, 10 lb. of potatoes, and 2 bags of mixed vegetables, paying a total of $16.95. Pat buys 3 gal. of milk, 2 dozen oranges, 1 dozen apples, 5 lb. of potatoes, and 5 bags of mixed vegetables, paying a total of $25.09. .... Find the cost of: 1 qt. of milk, one orange, one apple one lb. of ground beef, one lb. of potatoes, and one bag of mixed vegetables. Answered by Penny Nom. 





A ladder problem 
19990422 

From Michael Blade: There is a cube box 3feet x 3feet x 3ft resting against a vertical wall on level ground. Resting against the outside corner of the box is a ladder 10 feet tall, this ladder is of course resting on the ground but also against the outside corner of the box and rests on the wall. The question the ladder is divided into two unequal section bounded by the box to the ground and the box to the wall. what are those dimensions? Answered by Penny Nom. 





Quadratic equations 
19990331 

From Ken Niebergall: #1 a^{2}  10a = 2a  36 #2 t(t  5) = 5 (t  5) #3. (x + 4)(x  3) = 8 Thanks. Answered by Jack LeSage and Penny Nom. 





Standard Form 
19990330 

From Pam: How do you put this equation into standard form? y=3.572x+5.409 Would you please put this equation in this form Ax+Dy+C=0 Answered by Penny Nom. 





Linear Equations 
19990116 

From Casie Tomney: My dad and I have been trying to figure, how to solve for x on any of these problems my teacher gives us. The problem is: 2h/3 + 1/2 = 5h/6  3/4 Thanks!!!!!!!! Answered by Jack LeSage. 





Intersection of Planes 
19981203 

From Lindsay Fear: My name is Lindsay Fear. I am an OAC student (which is the Ontario equivalent to Grade 12 in most other states and provinces). I am in an Algebra and Geometry course and am currently studying a unit on equations of planes. Our teacher has given us this question that my friend and I have attempted several times, but we are still unable to solve it. My teacher has also suggested using the internet as a resource. The question is: Prove that a necessary condition that the three planes x + ay + bz = 0 ax  y + cz = 0 bx + cy  z = 0 have a line in common is that a^2 + b^2 + c^2 + 2abc = 1 Answered by Walter Whiteley. 





Algebra 
19981125 

From Casey: yeah my son brought home a math worksheet and he was wondering and me too if u could help him and me out . he has problems like this 4n+9=7n+2= ??? and he has to show work so if u could help us out that would be great Answered by Jack LeSage. 





Linear systems of equations 
19981116 

From Crystal Girvan: My name is Crystal Girvan.Im in grade 11. I have a question.We are solving linear systems of equations: comparison method. My questions is. it says a)use the method of comparison to solve this system a=b1, 3a+ b=3 b) verify your solutin in a I dont understand it. please help Answered by Jack LeSage. 





The Left Side of a Parabola. 
19981020 

From Shay: Find the parametrized equation for the left half of the parabola with the equation: Y=x^24x+3 Answered by Chris Fisher. 





A Linear System 
19981008 

From Jason Bussey: The linear systems with the following pattern all have the same solution. Is their some kind of reasoning as to why this is so? 2x+3y=4 3x+4y=5 4x+5y=6 5x+6y=7 The solution is always x=1, y=2 Thank you Jason Answered by Penny Nom. 





Grade 9 Algebra 
19980607 

From Tarah Kostenko: I am a grade 9 student and I cannot figure out how to solve these two similar problems. can you please help? 3(y1/2)=1/2 also 2/3(x + 1)=6 I don't come up with the same answers as the book and I can't figure out what I'm doing wrong. Thank you,
Answered by Harley Weston. 





Graph question 
19980512 

From Rose Seminary: Why is the point of intersection of two lines the solution to the corresponding system of equations? Answered by Penny Nom. 





Seed Problem 
19980326 

From Jody A. Johnson: Seed Problem: The height of an amazing plant grown from a seed varies linearly with the time it has been in the ground. After six days it is 6cm tall and after 60 days it is 15.8m (1580 cm) tall.  Write the particular equation giving the height as a function of time.
 Find the intercepts and explain them.
 What would be the height in one year?
 How long would it take for the plant to grow to a height of 1km?
I'm having a problem with this equation. Could you please help. Thank you. Answered by Penny Nom. 





Yintercept 
19980227 

From Don Trumpet: What is the Yintercept for the problem:Y = 2(x+2) + 9 Answered by Harley Weston. 





Intersecting Lines. 
19980210 

From Erik Heppler: My typewriter frequently makes mistakes. Suppose I gave you the following system of equations to solve: 35.26X + 14.95Y = 28.35 187.3X + 79.43Y = 83.29 When I looked back, I realized that I meant to use 14.96 as the "Y" coefficient in the first equation instead of 14.95. Solving the system using 14.95 and then solving another system using 14.96 with all other values the same both times results in the intersection points (1776, 4186) and (770, 1816) respectively. How can that be? Answered by Penny nom. 





Find the Numbers. 
19971228 

From Sandy C: The sum of the squares of two numbers is 53. Twice the greater, minus the lesser is 11. Find the numbers. Answered by Penny Nom. 





Equation of a line 
19970408 

From Susan Gregson: I am a secondary school teacher. My students and I would like to know why the letters m and b are traditionally used to stand for slope and Yintercept in the standard form of an equation. Was this an arbitrary choice? Who made it? Are the letters from Greek ot Latin words? Answered by Harley Weston. 





A Functional Equation. 
19970226 

From Ronald Lui: Find all functions f:S > S statisfying the two conditions: 1)f(x+f(y)+xf(y))=y+f(x)+yf(x) for all x and y in S 2)f(x)/x is strictly increasing on each of the interval 1 Answered by Saroop Kaul and Chris Fisher. 





Cardano's method 
19960311 

From Mike Gorski: What is Cardano's method for finding the roots of a cubic equation? Answered by Harley Weston. 





Un système de plusieurs équations et plusieurs inconnues 
20090122 

From Cédrick: J'ai un problème écrit à résoudre estce que vous pouvez m'aider ?
Le premier est le tiers de la somme des deux autres.
La somme du premier et du deuxième est 13.
Le produit du deuxième et du troisième est 56.
Réponse: Le premier nombre est___________________
Le deuxième nombre est _________________
Le troisième nombre est _________________
Answered by PierreLouis Gagnon, Antoine Letarte at Claude Tardif. 





Combien d'éleves fréquentent cette école? 
20080404 

From Jeff: Une ecole compte sept fois plus d'éleve que d'enseignants et enseignantes .De plus , le nombre de membres du personnel non enseignant correspond a la moitié du nombre d'enseignats et enseignantes . Si l'on tient compte de l'ensemble des éleves , du personnel enseignant et du personnel non enseignante , on dénombre 714 personnes . Combien d'éleves fréquentent cette école? Answered by Antoine Letarte. 





Système à deux équations 
20071211 

From Fabrice: un rectangle a 130 m pour périmetre. si on diminue sa longueur de 1 m et on augmente sa largeur de 1 m, l'aire augmentera de 14m².
trouver les deux dimentions du rectangle. (on trouvera, au préalable, la difference des deux dimensions) Answered by Claude Tardif. 





Des mots aux équations 
20061102 

From Julie: La diffÃ©rence de deux nombres, x et y est de 28. Le nombre y correspond aux huit neuviï¿½mes du nombre x. Trouvez ces deux nombres. Answered by Claude Tardif. 





Les equations 
19991209 

From Enciso Alberto: j'ai les equations suivantes: X1=Rs + A1/(B+W^2) X2=Rs + A2/(B+W^2) X3=Rd + A3/(B+W^2) X4=Rd + A4/(B+W^2) X5=Rg + A5/(B+W^2) X6=Rg + A6/(B+W^2) dont les coefficients Ai (i=1,2,..) et B sont constants (mais on ne conais pas leur valeur) et Rs, Rd, et Rg sont inconnues. Nous pouvons constater que la dependence de ces differentes expessions en fonction de W^2 est identique. Le tracé de l'une de ces expressions en fonction d'une autre est donc une driote. . . . Answered by Claude Tardif. 

