







The sum and difference of two numbers 
20170320 

From Olivia: The sum of two numbers is 87 and their difference is 29. What are the two numbers Answered by Penny Nom. 





A road trip word problem 
20160410 

From Marc: While on a road trip I imagined this random word problem. Suppose I start a trip of 75 miles. My initial speed is 75 miles per hour. After every mile traveled I decrease my speed by one mile per hour. After the first mile I decrease my speed to 74 miles per hour and so on for each subsequent mile traveled. How long will it take to complete the 75 mile journey? Answered by Penny Nom. 





The integral of a sum 
20160310 

From Rahul: How to solve definite integral of a sum. The specific problem is as follows,
Integral of ( 1+ sum of x^k, k=1 to k=n), x=0 to x=b *dx.
The answer is b + sum of b^(k)/k, k=2, to k=n+1. I understand only the integral
of first term. But integral of the sum I do not understand at all. Answered by Penny Nom. 





The sum of the angles of a triangle 
20160224 

From Sophia: Does every triangle add up to 180 degrees? (Such as a unique triangle) Answered by Penny Nom. 





Fractions of two quantities 
20160122 

From Melody: Kate ate 1/4 of her orange. Ben ate 2/4 of his banana. Did Kate and Ben eat 3/4 of theit fruit? Explain. Answered by Penny Nom. 





The sum of two repeating decimals 
20151022 

From Kaitlin: Here is the question I am struggling with:
Is the sum of two repeating decimals always repeating decimal? Explain your answer and give an example.
I answered this question thinking that no you cannot but only when adding 0.9 repeating, but my professor said this was incorrect.
Thanks for the help!
Kaitlin Answered by Penny Nom. 





1 + 2 + 3 + ... + (2n  1) 
20150101 

From Brian: Hi Maths Central
My wife presented me with a query which may have a simple answer, but one that I can’t deduce or explain.
Take the string of numbers, n=1,2,3,4,5…
It seems that n(2n1) = Sum((1…..(2n1))
e.g. for n=5, both 5 x 9 and Sum(1….9) equal 45, and so on for other values of n.
Could you please provide an explanation? Does it have an underlying reason and a name?
Look forward to your response.
Brian Answered by Penny Nom. 





Two quadratic polynomials 
20141028 

From khushboo: The zeroes of a quadratic polynomial x^2+ax+b are 'c' and 'd'
and the zeroes of a quadratic polynomial x^2+cx+d=0 are 'a' and 'b'.
find the numerical value of a+b+c+d where a, b, c and d are non zero integers. Answered by Penny Nom. 





The sum of two numbers is 52 
20140901 

From Blake: The sum of two numbers is 52 and the difference is 10. What are the numbers? i used to be real good at this stuff? Answered by Penny Nom. 





A price increase and a consumption decrease 
20140816 

From sujan: If the price of petrol increases by 25% and Rajesh intends to spend only 15% more on petrol then by how much % should he reduce the quantity of petrol he buys? Answered by Penny Nom. 





The combination of 6 numbers from 1 to 355 that gives us 360 
20140529 

From Ion: Hi,
My name is Ion and I am trying to find the number of combinations of 6 numbers (angles) that would sum to 360 (degrees).
Thank you! Answered by Robert Dawson. 





Two numbers whose difference is 16 
20130608 

From Johan: Two numbers whose difference is 16 and whose sum is 120 Answered by Penny Nom. 





1+2+4+8....= 1 
20120402 

From Andy: In this minutephysics video, it's claimed that 1+2+4+8....= 1
Is this true, and if so, how?
< href="http://www.youtube.com/watch?v=kIq5CZlg8Rg">http://www.youtube.com/watch?v=kIq5CZlg8Rg Answered by Robert Dawson. 





Sum and difference of squares 
20111231 

From Anne: Se x e y são números reais distintos, então:
a) (x^2 + y^2) / (x  y) = x + y
b) (x^2 + y^2) / (x  y) = x  y
c) (x^2  y^2) / (x  y) = x + y
d) (x^2  y^2) / (x  y) = x  y
e) Nenhuma das alternativas anteriores é verdadeira. Answered by Harley Weston. 





The sum of a series 
20111107 

From Rattanjeet: Find the sum of 1(1/2) + 2(1/4) + 3(1/6) + 4(1/6)(3/4) + 5(1/6)(3/4)2 + 6(1/6)(3/4)3+ ... where 1/6 + (1/6)(3/4) + (1/6)(3/4)2 + ... constitutes a geometric series. Answered by Penny Nom. 





4 + 10 + · · · + (6n − 2) 
20100421 

From Lan: Find the sum 4 + 10 + · · · + (6n − 2). The answer is 3(n^2) + n. How? Answered by Penny Nom. 





1/1+1/2+1/3... 
20100331 

From Mohd: you explained the way of getting the summation of 100 series numbers
but what is the summation of the numbers 1/1+1/2+1/3+1/4+1/5.............................+1/100 Answered by Robert Dawson. 





1^3 + 2^3 + 3^3 +4^3 ... n^3 = ? 
20100129 

From ireimaima: Hi..
Can u please help me with this question..
I find that when i test eg: n=2 for n (n+1) /4,
it seems that it does not giving me the right answer of 1^3 + 2^3 = 9
but 3/2... i'm confuse..can u please help me..thanks so much
Prove that:
1^3 + 2^3 + 3^3 +4^3………………………………..n^3 = n (n+1) /4 Answered by Penny Nom. 





Odds and evens in an n by n+1 table 
20100121 

From Shankar: The boxes of an n * (n+1) table ( n rows and n+1 columns) are filled with integers.
Prove that one can cross out several columns ( not all of them !) so that after this operation
all the sums of the numbers in each row will be even. Answered by Robert Dawson. 





Summation Notation 
20091228 

From MANDIRA: I want to get the formula for expressing one number by summation of consucutive numbers . Answered by Janice Cotcher. 





Jill and Bill 
20091104 

From Lisa: Jill and Bill are two members of the Hill family. Jill is 8 years old and Bill is 9 years old. What will Bill's age be when the total of the digits in both their ages is once again 17? Answered by Stephen La Rocque. 





Arithmetic Sum & Sequence 
20090901 

From Alice: Find the 24th term of this sequence
6.8,8.0,9.2...
Find the sum of the first 21 terms Answered by Janice Cotcher. 





The sum of the angles of a triangle 
20090518 

From mary: prove that the sum of the three angles inside any triangle always add up to 180 degrees? Answered by Harley Weston. 





The sum of the roots of a quartic 
20090421 

From dave: This is a algebra problem that i am confused about:
The sum of the roots of x^4x^3+5x^2+4=0 is:
i tried graphing it, but it shows that there are no roots, but the answer is 1. are they wrong? Answered by Penny Nom. 





The sum of the roots of a quartic 
20090103 

From peter: How do you find the roots of an equation without graphing? like, i have a problem that says what is the sum of the roots of x^4x^3+5x^2+4=0. Answered by Harley Weston. 





Determining the Unknown Numbers 
20081206 

From jacob: the sum of two numbers is 45 and their difference is 15. what are the two numbers? Answered by Janice Cotcher. 





The distribution of sample sums 
20081121 

From Mark: For large samples, the sample sum (Σ x) has an approximately normal distribution.
The mean of the sample sum is n*μ and standard deviation is (σ*√n). The distribution of savings per account for savings and loan institution has a mean equal to $750 and a standard deviation equal to $25. For a sample of 50 such accounts, find the probability that the sum in the 50 accounts exceeds $38,000. Answered by Penny Nom. 





Factoring 
20081119 

From Neji: How do you factor (yz) (y+z) (y^4+y^2z^2+z^4) and get (y+z)(y^2yz+z^2) (yz) (y^2+yz+z^2) as the answer? Answered by Harley Weston. 





Intercepts 
20081102 

From robert: What is the sum of the xintercept and yintercept of the line 3x3y=24? Answered by Stephen La Rocque. 





An arithmetic series 
20081017 

From Laura: In an arithmetic series 5+9+13+...+tn has a sum of 945. How many terms does the series have?
What formula do I use? Answered by Penny Nom. 





Factoring x^2 + 729 
20080819 

From peter: hello I,am having trouble factorising a polynomial into polynomial factors
with real coefficients please can you help the polynomial is x^2+729 Answered by Harley Weston. 





Product of TwoDigit Numbers 
20080731 

From pete: The number 4641 can be expressed as the product of two twodigit whole numbers. What is the sum of these two numbers? Answered by Janice Cotcher. 





Sum and product of the roots of a quadratic 
20080703 

From Gautam: If a and b are the roots of x^2+px+1=0 and c and d are the roots of
x^2+qx+1=0
prove that
(ac)(bc)(a+d)(b+d)=q^2p^2
Regards
Gautam Answered by Harley Weston. 





The sum of the digits of twodigit number is 9 
20080701 

From Audrey: the sum of the digits of twodigit number is 9. if the digits are reversed, the new number if 63 greater than the original number. find the number. Answered by Penny Nom. 





111...111 * 2003 
20080623 

From Peggy: Number a = 111...111 formed by 2003 1's. Find the sum of the digits of the number 2003 * a. Answered by Penny Nom. 





The sum of the digits of a number 
20080623 

From Ben: Question: Using mathematical induction, prove that if the sum of the digits of a number is divisible by three, then the number itself is also divisible by 3. Answered by Penny Nom. 





The sum and product of the roots of a quadratic 
20080316 

From Katelyn: Write the quadratic equation....
Sum of the roots = 16
Product of the roots = 80 Answered by Penny Nom. 





Sum and difference of cubes 
20080130 

From Amanda: It has been a really long time since I was in Algebra and I can't remember how to factor cubes such as x^3 +81 or subtracting/adding fractions with variables such as [1/(x+h)+2][1/x+2]. Please help!!! Answered by Penny Nom. 





Total payments for a loan 
20071011 

From Robin: A person is going to arrange a loan at 3 mill. he will pay 150000 back each year , so it
take 20 yrs. to finish. In addition he pays 5% interest of what is leaft each year.
How do I find the sumfunction which shows the total sum he have payed? Answered by Stephen La Rocque. 





Sum and difference of two mystery numbers 
20071004 

From Donna: The sum of two numbers is 39. The difference is 11. What are the numbers? Answered by Stephen La Rocque. 





Ttotals 
20070926 

From Asma: I wanted to know what i should include in my Ttotals maths coursework and also how i should lay out the coursework? Answered by Penny Nom. 





Period of a sum of trig functions 
20070617 

From Aakash: the period of the function f(x)=cos3x+sin4x+tan4x Answered by Stephen La Rocque. 





Buying topsoil 
20070516 

From Claudia: I am trying to figure out if it is cheaper to buy topsoil by the bag (one 40lbs bag for $1.66) or having it delivered for $60 for 4 cubic yards. Answered by Penny Nom. 





The sum of two numbers is 30 
20061103 

From GG: The sum of two numbers is 30 and the product of the same two numbers is 221. Find the two numbers. Answered by Stephen La Rocque. 





How does knowing the sum for 2+7 help you find the sum for 6+1 
20061026 

From Andrea: How does knowing the sum for 2+7 help you find the sum for 6+1 Answered by Haley Ess. 





The odd numbers from 30 to 80 
20060921 

From Kieran: If you added all the odd numbers from 30 to 80, would the answer be even or odd? Explain.
I think it would be odd because I used this equation:
(30 x 5)+(40 x 5)+(50 x 5)+(60 x 5)+(70 x 5)+(25 x 5)=1325
I used the numbers for each set of ten 30 to 80 times 5 and the amount of the endings1,3,5,7,9 added, times 5. Is that right? Answered by Penny Nom. 





What is the sum of the first 100 whole numbers? 
20060531 

From Jo: what is the sum of the first 100 whole numbers? Answered by Natasha Glydon, Paul Betts and Penny Nom. 





Marine shipping  fuel consumption 
20060426 

From Sandy: When a ship is 800 nautical miles from port its speed is reduced by 20%,
thereby reducing the daily fuel consumption by 42 tonnes and arriving in
port with 50 tonnes onboard. If the fuel consumption per hour is given
by the expression (0.136 + 0.001V^3) where V is speed in knots;
Estimate a) reduced consumption per day b) fuel onboard when speed reduced
c) normal consumption for 800 nautical mile voyage d) increase in steaming
time Answered by Stephen La Rocque. 





Adding consecutive numbers 
20060426 

From Lisa: When I have a total that is the sum of consecutive numbers, how do I figure out what the numbers are?
Answered by Stephen La Rocque. 





Proving a summation formula by induction 
20060419 

From Sharon: Prove by induction that the sum of all values 2^i from i=1 to n equals 2^(n+1)  2 for n > 1. Answered by Stephen La Rocque. 





Arithmetic Sums 
20060412 

From Angel: (a) In a particular arithmetic sequence, u6 = 344.5 and u20 = 88.3. Find S28.
(b) In a particular arithmetic series, S10 = 495 and S15 = 1005. Express S15 in sigma notation. Answered by Stephen La Rocque. 





Sum of a Geometric Sequence 
20060411 

From Andre: In a particular geometric sequence, U3=3.6 and U10=12.9. Find S16 and S17. Answered by Stephen La Rocque. 





Factor 
20060308 

From Brad: Factor:
x^{3} + 64m^{3} and 125p^{3}  q^{6} Answered by Penny Nom. 





Josh and John were both exposed to the flu 
20051216 

From Dudley: Josh and John were both exposed to the flu. John has a 25% chance of getting it, while Josh has a 75% chance of getting it. What are the chances that at least one of them has the flu?
Answered by Penny Nom. 





Adding improper fractions 
20051125 

From Paula: I would like a simple step by step explanation on how to add improper fractions. Answered by Penny Nom. 





A block pyramid 
20051105 

From Kyle: if i make a block pyramid and it puts a new perimeter around it every time, for example the first layer will be 1 block across (area=1), the second layer will be 3 blocks across (area=9), the third layer will be 5 blocks across (area=15),etc. The normal block pyramid. I have figured out that in order to figure out the number of blocks needed for a certain level, the equation is (2x1)2 or (2x1)(2x1), where x is equal to the level. For example, on the fourth level, the equation tells you that it will have an area of 49. How would i make an equation for the total number of blocks up to the level. For example, in order to complete 1 level you need 1 block, for 2 levels you need 10 blocks, for three levels you need 35 blocks, and for 4 levels you need 84 blocks. Answered by Penny Nom. 





A sum of 75 and a difference of 13 
20051030 

From Vicki: Find two numbers that have a difference of 13 AND A SUM OF 75? We need to learn about the formula or procedure. Answered by Penny Nom. 





What is the sum of the measures of the angles of a decagon? 
20051015 

From Dianna: What is the sum of the measures of the angles of a decagon? Answered by Penny Nom. 





Two groups that have equal sums 
20050930 

From Anita: using the numbers 1, 2, 3, 4, 5, 6, 7,and 8. how do we divide them into two groups so that they have equal sums? Answered by Penny. 





How to add three addends 
20050928 

From Patricia:
explaination of how to add three addends if you use a double to add or if you use a sum of 10
8+3+2=
6+4+0=
3+3+6=
2+5+4=
Answered by Baul Betts and Penny Nom. 





The sum of a series 
20050831 

From Aamod: Find the sum of the given series till n terms:
(1^{4}\1*3) + (2^{4}\3*5) + (3^{4}\5*7)............... till n terms Answered by Chri Fisher. 





A set of numbers whose sum is 1 
20050721 

From Santos: Does there exist a set of numbers whose sum is 1, and the sum of whose squares is less than 0,01? Answered by Paul Betts. 





The sum of the digits of 2^100 
20050611 

From Richard: The sum of the digits was calculated for the number 2100, then the sum of the digits was calculated for the resulting number and so on, until a single digit is left. Answered by Penny Nom. 





Adding consecutive integers 
20050513 

From Yas: i need some help with my work which is to investigating sums of consecutive numbers for example: 15= 4+5+6 and 15=1+2+3+4+5 Answered by Penny Nom. 





Two matrix problems 
20050330 

From Sue: Question 1
Suppose all matrices in the equation below are square and invertible. Solve for x .
BA1XB1 + 2BA + In = 0 (the symbol "0" here denotes the matrix of all 0's in it)
Also, A1 or B1 is indicating inverse and "In" = for example, A1 times A
I hope you understand the above. I have to show all the steps.
Question 2
Suppose we consider the set of all 2x2 matrices along with the operations of matrix addition and multiplication. Do they form a field? Why or why not?
I think the answer is no because under multiplication it is not commutative and not all square matrices are invertible. I not positive so I'd like some help. Answered by Penny Nom. 





A product equals a sum 
20050327 

From Tor: Can you please help me with a general formula for the following system:
2+2=2*2
3+3/2=3*3/2
4+4/3=4*4/3
and how will you prove the formula?
Answered by Penny Nom. 





The sum of the digits 
20050316 

From kelsey: What is the sum of the digits in the decimal form of 2^{1999} * 5^{2002}? Answered by Claude Tardif. 





A matrix construction problem 
20050314 

From Marcelo: I want to know if is it possible to solve this problem:
I have an empty NxM matrix and I know totals (sum) by rows and totals by column.
Is there any algorithm to fill the matrix so that the summary of columns and rows gives the original values I have? Answered by Harley Weston. 





Sum to n terms of the series i.(2^(ni)) 
20050128 

From Satya: Sum to n terms of the series i.(2^{ni}) Answered by Penny Nom. 





1+3+5+...+(2n+1) 
20040910 

From Emma: Prove that 1+3+5+...+(2n+1)= (n+1)^{2} Answered by Penny Nom. 





Factoring 
20040719 

From A student: Factor completely:
3x3  24y3
54x6 + 16y3
16xy  4x  4y  1
0.09x2  0.16y2 Answered by Penny Nom. 





The sum of some positive integers 
20040607 

From A student: Find the sum of all positive integers not greater than 10000 that are divisible by neither 3 nor 7. Answered by Penny Nom. 





The sum of 4,0,4..., 156 
20040428 

From Christina: find the requested sum of the arithmetic sequence
4,0,4..., 156 Answered by Penny Nom. 





Factoring 
20040427 

From Bipin: FACTORISE:
a to the power of 6 + b to the power of 6 Answered by Penny Nom. 





Some factoring problems 
20040415 

From KJ: Factor these:
x^{3}+125 > (x+5)^{3}
8x^{3}27 > (?)
x^{2}+36 > (x+6)^{2}
x^{4}5x^{2}+4 > (?) Answered by Penny Nom. 





Sum of the angles in a pentagon 
20040311 

From Ashish: What is the sum of all the measures of the angles of a Pentagon Answered by Penny Nom. 





Sums and differences 
20040210 

From David: The sum of two whole numbers is 63. The difference between the numbers is 10. Find all the possible pairs. Answered by Claude Tardif and Penny Nom. 





The sum of two numbers is 5 and their difference is 
20030616 

From Akhil: The sum of two numbers is 5 and their difference is 11. What is the product of the two numbers? Answered by Penny Nom. 





positive multiples of 10 that are the sum of four consecutive integers 
20030501 

From Taurus: How many positive multiples of 10 that are less than 1000 are the sum of four consecutive integers? Answered by Penny Nom. 





Three digit number 
20030310 

From Grace: What three digit positive integer is exactly 32 times the sum of its digits? Answered by Claude Tardif. 





Factoring 
20021211 

From Larry: Question:
how do u factor trinonmials
EX: X^{ 3} + Y^{ 3}
X^{ 3}  8Y^{ 3}
8X^{ 2}  72
64A^{ 3}  125B^{ 6} Answered by Penny Nom. 





Factor completely 
20021121 

From Shelley: these two questions are to be factored completely but i have no idea how to factor them  (x4y)^{ 2}  3(x4y)  4
 x^{ 6} + y^{ 6}
Answered by Penny Nom. 





Fuel consumption 
20021111 

From Guy: When a car is driven 'normally' the feul consumption is 7.5 per litres per 100km. On a particular journey the car was driven in 'hard' and the consumption changed to 9.1 litres per 100km. Fuel cost 80p per litre. Calculate:
a) The extra feul consumed. b) The extra cost of feul, in pounds, for the journey when the car was driven in 'hard'. Answered by Penny Nom. 





Sums of evens 
20020914 

From Rosa: How do I find a geometric way to easily compute sums of consecutive even numbers 2 + 4 + 6 + .... Answered by Leeanne Boehm and Harley Weston. 





7+8+9+...+1000 
20020911 

From Shirley: My question is what is the formula for adding up numbers when you don't start with number 1? For example 3 + 4 + 5 + 6 = 18. But how could you arrive at the answer without adding all the numbers? Answered by Penny Nom. 





The sum of the first one hundred even numbers 
20020910 

From Arthur: What is the sum of the first one hundred even numbers? Answered by Penny Nom. 





The sum of the areas of two regular decagons 
20020527 

From A parent: The sum of the areas of two regular decagons is 39 square inches, and their radii are in the ratio of 2:3. Find the area of the larger decagon. Answered by Paul Betts. 





Arithmetic progressions 
20020424 

From David: I have been searching everywhere for the formula to mathamatical progression. Answered by Penny Nom. 





24x^4 + 3x 
20020318 

From gary: 24x^{ 4} + 3x Answered by Penny Nom. 





1+2+3+...+1000 
20011001 

From Louise: Find a quick way to add all Intergers (whole Numbers) between 1 and 1000? Answered by Walter Whiteley. 





Conservation, consumption and population growth 
20010604 

From Steve: I'm trying to quantify the relation between conservation/consumption and population growth. For instance let's consider California: The 2000 census states that California's population grew from 29,760* in 41990 to 33,871 in 42000. I want to find r or rate of growth per year. Based on the exponential growth formula for population growth: . . . Answered by Penny Nom. 





Marginal Propensity to Consume 
20010509 

From Esther: The derivative of the national consumption function C = f(y) is called the ____________________. Answered by Judi McDonald. 





National consumption function 
20010509 

From Brian: If consumption is $11 billion when disposable income is 0 and the marginal propensity to consume is dC/dy = 1/(2y+4)1/2+0.3(in billions of dollars), find the national consumption function. Answered by Harley Weston. 





Sigma 
20010331 

From A student: What does the Sigma symbol mean in mathematics? Answered by Penny Nom. 





The sum of all tendigit numbers. 
20010110 

From John: Compute the sum of all tendigit numbers. Can you determine the sum of all n digit numbers? Answered by Sukanta Pati. 





A dollar, quarter, dime, nickle and penny 
20010107 

From Sarah: Arnold has a dollar coin, one dime, one quarter, one nickel, and a penny. The number of different sums of money that can be formed using three coins is... Answered by Penny Nom. 





Infinite Geometric Series 
20001110 

From Sam Carter: I ran into a problem when studying how to find the sum of an infinite geometric series. My math book attempts to explain the concept by giving formulas involving sigma and r, but it does not really explain how to go about finding the sum of an infinite geometric series. If you could either help me with this or point me in the direction of an informative website that could help me, I'd appreciate it. Answered by Harley Weston. 





The sum of the cubes is the square of the sum 
20001010 

From Otoniel: Without using mathematical induction, or any other method discovered after 1010 a.d. , prove that the sum of i^{3}, (where i, is the index of summation) from one to, n, is equal to ((n*(n+1))/2)^{2} Answered by Penny Nom. 





1 + 2 + 3 + ... + 50 
20000914 

From Vicki Charron: How can you calculate the total of the numbers one through fifty, without adding up the individual numbers? Answered by Penny Nom. 





The sum of the squares of 13 consecutive positive integers 
20000825 

From Wallace: Prove that it is not possible to have the sum of the squares of 13 consecutive positive integers be a square. Answered by Harley Weston. 





Riemann sums 
20000330 

From Joshua D. Parham: If n is a positive integer, then
lim (1/n)[1/(1+1/n) + 1/(1+(2/n) + ... + 1/(1+n/n)]
n>infinity
can be expressed as the integral from 1 to 2 of 1/x dx Answered by Penny Nom. 





The sum of the cubes is the square of the sum 
19990825 

From Bernard Yuen: How to prove 1^{3} + 2^{3} + 3^{3} + 4^{3} + ... n^{3} is equal to (1+2+3+...n)^{2}? (for n is positive integer) Answered by Harley Weston. 





Compound Interest 
19990701 

From Kim Palmer: In early 1997, my son borrowed $4831 at 7.5%. He has made 30 monthly payments of $130 each. He is now in a position to pay off the balance. What is his remaining principal? Answered by Penny Nom. 





Factoring 
19990330 

From Maggie Stephens: I don't know anything about factoring would you plese help me. 3x^{4}  48 54x^{6} + 16y^{3} 1258x^{3} 12x^{2}  36x + 27 9  81x^{2} a^{3} + b^{3}c^{3} I would greatly appreciate any help you can give me thanks. Answered by Jack LeSage. 

