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Working with percentages 2018-08-26
From Kenneth:
16 is 4% of what amount? The answer can be determined by the following unusual manner: 4% = 16 1% = 4 100% = 400 Can the following solutions for the following be determined by using the same type of calculation? 16 is ?% of 400 ? is 4% of 400 I thank you for your reply.
Answered by Penny Nom.
How many pet dogs? 2017-09-26
From Michelle:
In 2016 there were about 135 million households in the United States. 36.5% of the households own at least one dog. On average, these households have 1.6 dogs. How many millins of pet dogs were in the United States in 2016?
Answered by Penny Nom.
The ratio of two ages 2017-03-15
From Angel:
The sum of Keith's age and Alan's age is 36. Four years ago, the ratio of Keith's age to Alan's age was 4:3. Find the ratio of their present age
Answered by Penny Nom.
The ages of 10 children 2016-08-17
From Diann:
Sum total of the ages of 10 children 10 children is 110, what are their ages if all are 2 years apart?
thank you

Answered by Penny Nom.
A percentage problem 2016-03-02
From jehanzaib:
if x is a percentage: e.g. 40% than what does "x/(1+x)" = 29%. what is the explanation.
Answered by Penny Nom.
Three discounts 2016-01-10
From Tiffany:
Khairul wants to buy a sofa set. He is offered 3 successsive discounts of 10%,20% and 25%, and he can arrange them in any order he wants. Which order will benefit him the most? Explain your answer.
Answered by Penny Nom.
A troublesome word problem 2015-12-28
From Linda:
James is now 3/5 John's age. Three years ago, he was 1/2 John's age. Three years from now, he will be 2/3 John's age.
How old are they now?

Answered by Penny Nom.
A word problem with percentages 2015-12-05
From Caedryn:
After giving 25% of her stickers away, May had 50% as many stickers as Rose. If they had 200 stickers altogether at first, how many stickers did Rose have?
Answered by Penny Nom.
An increase in savings 2015-09-06
From A student:
A man spends 80% of his income. His income increases by 40% and his expenditure also increases by 25%. Find the percentage increase in his savings?
Answered by Penny Nom.
Rates, percentages and units 2014-12-30
From Kenneth:

If percentages have no units, why are some percentages called rates, as in interest rate, or perhaps a tax rate of 7% as an example? A rate has units of different quantities.

I thank you for your reply.

Answered by Robert Dawson.
Percentages in a mixture 2014-10-02
From viola:
Hi there

can you help me convert the below so it makes 100% (individual %)

400 gr =
100 gr =
50 gr =
50 gr =
20 gr =
2 gr =
1 gr =
1 gr =

Be great to hear back from you

Thank you


Answered by Penny Nom.
The average of 9 numbers is 45 2014-09-12
From rizza:
The average of 9 numbers is 45. If 90 and 88 are added to the set of numbers. What will be the resulting average?
Answered by Penny Nom.
What is the average of first 100 even numbers? 2014-08-02
From Faizan:
What is the average of first 100 even numbers?
Answered by Chris Fisher.
A word problem concerning averages 2014-07-26
From Bernie:
The average weight of a team of children is 50kg, Todd who weighs 56 kg then joins the team. The average weight of the new team is 51. How many children in the original team?
Answered by Penny Nom.
4 children 2013-12-31
From hope:
4 children; Peter is 7 years old & is 4 years younger than Dave. Dave is 9 years older than Paul. Paul is 11 years younger than Frances. Please list the children in order from oldest to youngest?! thank you and anxiously await your answer, Hope
Answered by Penny Nom.
Solve for x 2013-10-12
From Megan:
X\2400. Times 100=40%. What is x?!
Answered by Penny Nom.
What percent is 50 of 4.5 billion? 2013-08-08
From Bobby:
What percent is 50 from 4.5 billion?
Answered by Penny Nom.
Markup and discount to get a sale price 2013-03-02
From Warren:

If you are an ardent shopper you will be aware of the discount (% decrease) marketing strategy to produce the sale price. I began to wonder just how much mark-up (% increase) was added initially to an item in order to deliver the discounted sale price.

It was simple to construct a formula to convert one to the other.

For example a 30% (mark down) decrease in price required a 42.86% (mark up) to increase the price initially to Tag price. However when I started apply the formulae to a number of circumstances I noticed some very interesting circumstances associated with this relationship

For example a 99.999999% decrease is numerically equal to a 9,999,999,925% increase (huge ratio difference) while conversely a 0.1% decrease is numerically equal to a 0.10010010% increase (Infinitesimally small ratio difference) so the patterns appears logarithmic not linear.

However what really caught my attention was this pattern

See http://www.ozsmart.com/doc/percentage.htm

My questions is why does the decline in the ratio of increases in required mark up (%) price peak at 50 and 51% precisely and then expand again as the percentage move higher

Any explanation would be appreciated

Answered by Harley Weston.
A Performance Appraisal 2012-03-06
From Reuel:

I'm looking for an answer to this one:

If I have 428 staff for Performance Appraisal the year 2011 my suggestions for rating their rankings would be:
5% can be no. 1 which would mean 21 employees
15% can be no. 2 which would mean 64 employees
60% can be no. 3 which would mean 257 employees
15% can be no. 4 which would mean 64 employees
5% can be no. 5 which would mean 21 employees
However, what I have received is this:
5% are no. 1 which would mean 20 employees
22 % are no. 2 which would mean 94 employees
60% are no. 3 which would mean 270 employees
15% are no. 4 which would mean 41 employees
5% are no. 5 which would mean 3 employees

Now my question is how do I find the percentage difference between both the scenarios of should be versus reality? I don't think it is normal subtraction, is it? any help would be appreciated.

Best Regards,

Answered by Harley Weston.
[Difference between percentages and percentages] 2012-03-06
From Reuel:

I'm looking for an answer to this one:

If I have 428 staff for Performance Appraisal the year 2011 my suggestions for rating their rankings would be:
5% can be no. 1 which would mean 21 employees
15% can be no. 2 which would mean 64 employees
60% can be no. 3 which would mean 257 employees
15% can be no. 4 which would mean 64 employees
5% can be no. 5 which would mean 21 employees
However, what I have received is this:
5% are no. 1 which would mean 20 employees
22 % are no. 2 which would mean 94 employees
60% are no. 3 which would mean 270 employees
15% are no. 4 which would mean 41 employees
5% are no. 5 which would mean 3 employees

Now my question is how do I find the percentage difference between both the scenarios of should be versus reality? I don't think it is normal subtraction, is it? any help would be appreciated.

Best Regards,

Answered by Harley Weston.
Tina is older than Catherine by 1 year and 7 months 2012-03-03
From jennifer:
Tina is older than Catherine by 1 year and 7 months. Karen is younger than Tina by 2 years and 11 months. If Karen is 7 years and 2 months old, find out Catherine's age.
Answered by Penny Nom.
Find his income on the fourth week of August. 2011-03-22
From Abeth:
The average weekly income of MJ for the first three weeks of August was 3,600 and his average weekly income for four weeks is 3950. Find his income on the fourth week of August.
Answered by Penny Nom.
The new diameter is 50 per cent larger than the original. 2010-09-04
From mahwish:
. A circular logo is enlarged to fit the lid of a jar. The new diameter is 50 per cent larger than the original. By what percentage has the area of the logo increased?
Answered by Tyler Wood.
$1579 is 20% of what number? 2010-07-22
From Luis:
Question: $1579 is 20% of what number?
Answered by Robert Dawson.
Comparing percentages 2010-06-14
From Anouska:
In category A, Annie gave 5 out of 6 responses. I make this 83% I the same category, Adam gave 4 out of 10 responses. I make this 40%

Does this mean that Annie gave 43% more responses in this category than Adam?

Answered by Robert Dawson.
The average over two semesters 2010-01-20
From edy:
6 courses have an average of 100 in the first semester 5courses have an average of 90 in the second semester what is the average of the two semester , method of calculation , how come to have 95.4545
Answered by Penny Nom.
Jill and Bill 2009-11-04
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.
Averaging percentages 2009-06-14
From Alan:
Can you add percentages and then divide them by the number of percentages to get the average percentage. I.E day 1 100% day 2 100% day 3 95% average= 98.3%

is the above possible or is it not done, I have a dispute with a work colleague over this.

many thanks

Answered by Harley Weston.
Can you convert numbers with units to percents? 2009-02-12
From Kenneth:
To change a number to a percent, move the decimal two places to the right and add a percent sign. For example, 0.35875 = 35.875%.
If the number has a dollar sign or some other kind of unit, for example, pounds, feet, etc. how is the number converted to a percentage.

For example, change $0.35875 and 0.75 lbs. to a percentage. How is this done. I have never seen $35.875% or 75 lbs.% before.

Answered by Robert Dawson and Harley Weston.
A company fish fry 2009-02-04
From shaelisa:
At a company fish fry, ½ in attendance are employees. Employees’ spouses are 1/3 of the attendance. What is the percentage of the people in attendance who are not employees or employee spouses?
Answered by Robert Dawson.
A different approach to a word problem 2008-10-03
From Kenneth:
Sarah's age is 2/3 of Mary's age and 3/4 of Ruth's age. The sum of their ages is 46 years. How old is each?
Answered by Penny Nom.
How old are Brett and Jenny ? 2008-08-28
From Todd:
Brett and Jenny are each 10 years old. The sum of their ages is 11. Brett is 5 years older than Jenny. How old are they?
Answered by Janice Cotcher and Victiria West.
What percent of the 35 graduates took the exam? 2008-04-25
From Laura:
I have 35 graduates. All but 2 took their board exam. What percent of the 35 graduates took the exam?
Answered by Stephen La Rocque.
How old is the 11th person? 2007-12-08
From Jamie:
Ten people are in a room, and their mean age is 15. After another person enters the room, the mean age is now 18. How old is the person that walked in?
Answered by Jesse McLeod and Stephen La Rocque.
Fractions, ratios and percentages all mixed together 2007-08-29
From Charon:
x : 1/4% :: 9 3/5 : 1/200

Answered by Stephen La Rocque.
income percentages 2007-02-05
From karen:
I would like to know what percent of a bill each person would pay based on the income differences one person makes 78968.00 and the other makes 52000.00 I believe it is 65% and 35%

so if a bill is 120.00 one person pays 78 and the other pays 42 is this correct thanks

Answered by Stephen La Rocque.
27 snakes in four cages 2006-12-05
From Sherril:
A zookeeper has to put 27 snakes in four cages. His problem is that he must have an odd number of snakes in each cage. How can he accomplish this? You can put any number of snakes in a cage as long as the total number of snakes in each cage is an odd number.
Answered by Stephen La Rocque and Penny Nom.
Grossing up payroll wages 2006-08-27
From Katie:
I really need to understand (spelled out step by step) how to gross up payroll wages.
Answered by Penny Nom.
Power walking 2006-07-30
From Wendy:
I have an exercise routine of 'power walking', approx. 5-6 days per week. I carry a pedometer with me during these walks so that I can keep track of the distance of each walk. I've created a weekly walking chart on my computer, so each time I get back from a walk, I enter my stats, such as kilometers and miles walked that day, as well as my start and finish time. At the end of each week, before I printed out my completed chart, I would calculate out what my average walking distance was, for that particular week.

At the end of each month, I would calculate:
[1] I'd add up my total kilometers and miles walked for that month. (a no brainer ~ I could do that one!)
**But also, I would work out the percentages of the following:
[A] What my average daily distance p/walk was, for that month
[B] What my average time spent, per walk was, for that month

Answered by Penny Nom.
Rates and percentages 2006-06-20
From Todd:
If rates are about to rise 1.84%, from the current 5.30% that they are currently at. What amount are they going to increase to?

I ask because many publications print an answer that is 7.14% but I don't see that as correct because the first line would have to say an increase of 184 basis points for that to be correct. My answer to this is about 5.4%. Am I thinking correctly?

secondly, if rates are about to move to 7.14% from 5.3% what percentage move is this?

I get an answer of about 35%. am I off on this or is everyone else that I ask not calculating correctly?

Answered by Claude Tardif.
What's the difference between percentages and points? 2006-04-21
From Sayed:
What is the difference between percentages and points?
Answered by Stephen La Rocque.
The average of monthly averages 2006-04-06
From Ray:
I have the averages of some data in percentages. the data is rather large, how can i find the average of these averages without going back to the original data? Is there a Factor or Constant that i could multiply or devide or add and get the average of these averages without resorting to the raw data.
Answered by Steve La Rocque and Harley Weston.
Superimposing images 2006-03-30
From Laurie:
I am a parent and trying to find real world applications for the math strand that includes superimposing one item on another to determine identical. The Alberta strand is match size and shape of figures by superimposing one on top of the other. I am trying to find a way to put this into context for everyday life. Any ideas?
Answered by Penny Nom.
Working with percentages 2006-02-10
From Mark:

Hi, i have problem...i am trying to average a group of numbers....when i try to average the average...its gives a different results:

A b c d = A/(b-c)
1169 1173 1 100%
534 540 0 99%
358 359 0 100%
172 174 0 99%
. . . .
. . . .
. . . .
2375 3422 24 70%
1976 3677 42 54%
1431 3660 53 40%
187 3433 57 6%
761 3142 39 25%
2080 2109 7 99%
38280 49121 266 78.35%

When I try to average column D - it yields to 86.73% and not 78.35?

Please help me

Answered by Penny Nom.
More on percentges 2006-02-10
From Rich:
I need to dilute several owners who combined own 66% down to 50% and increase the 34% owner to 50%. I thought it was as simple as taking 16% away from each of the 66% and transferring that amount to the 34%, but it doesn't add up.
Answered by Penny Nom.
Percentages in our daily life 2005-12-23
From Naina:
what are the uses of percentages in our daily life
Answered by Penny Nom.
Mario is 16 years older than his youngest sister, Mercedes. 2005-11-08
From Jennifer:
Mario is 16 years older than his youngest sister, Mercedes. Together, their ages total 36 years . How old is each person?
Answered by Paenny Nom.
Wages for one month 2004-09-20
From Janet:
if offered $10,000 or 1 cent on the first day and then doubled daily for one month which would you take ?
Answered by Harley Weston.
Percentiles 2004-08-15
From Gary:
Table 1 Selected percentiles for family income in the US in 1992 1 $1,300 10 $10,200 25 $20,100 50 $36,800 75 $58,100 90 $85,000 99 $151,800

Q. The percentage of families in Table 1 with incomes below $58,100 was about?

Answered by Penny Nom.
English 2004-05-27
From Chang:
well my question is i was told by most of the teachers that ''think in english'' is the best way to learn english but how can i do like that do i need to know about the stucture first or do i need to learn the western culture ?

here is a sentence i have translate directly from my mother language.'' i was given an admiration of sincerity from this client on the follow up action i have done in the complaint.

Answered by Claude Tardif.
Differences in percentages 2004-04-06
From Jose:

You have two groups:

Group A has 10 people and 2 are Chinese
Group B has 12 people and 3 are Chinese

In terms of percentages what is the difference in Chinese between the two groups? In other words which group has the biggest percentage of Chinese and why?

Answered by Penny Nom.
Adding percentages 2003-12-19
From Paula:

How do you add percentages

e.g 90% + 80% + 60% + 54% + 25% = ?

Answered by Penny Nom.
The product of the page numbers 2003-11-07
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.
Means 2003-10-28
From Abdu:


The average of the 8 numbers listed above is 88. Of the following which pair of numbers could be removed from the list without changing the average.

A. 80 and 97
B. 80 and 98
C. 84 and 92
D. 84 and 97
E. 85 and 92

Answered by Andrei Volodin and Penny Nom.
Knitting gauge and felting 2003-10-27
From Sara:

I wish to create a pattern to knit an item that will then be felted, thus, shrink as a result. In order to determine the proper gauge to use in creating the item, I produced a gauge swatch, noted the original properties and then the post-felting properties. They are as follow:

Before Felting:

20 stitches(width) x 20 rows(height)yielded:
Gauge: 3.2 stitches(width) and 4 rows(height) = 1"
Dimensions: 6.25"(width) x 5.25"(height)

After Felting:

20 stitches(width) x 20 rows(height)
Dimensions: 4"(width) x 3"(height)

How do I calculate the percentage change in size to accurately determine the number of stitches and rows needed to produce the desired dimensions for the finished (felted) item?

Answered by Penny Nom.
Averages of Averages 2002-12-21
From Amy:
If in the month of October the % of Payments Received was 80.74% and in November it decreased to 69.36%. Can you take the 80.74-69.36/69.36 to get the % of difference. In otherwords can you take the % of difference when the numbers you are comparing are %'s????

Can you also take an average of an average? For example, average number of payments received in October was 25.00%, average number of payments received November was 50.00%, and the average number of payments received in December was 15.00%. Do you average (25.00%, 50.00% and 15.00%) or do you have to go back to the numbers that calculated the averages. For example, October 25.00% was based on 25 payments being received out of a possible 100. So instead of taking the average of the averages, do you take the average payments and the average customers over the 3 months and calculate the average???

Answered by Harley Weston.
Nixon, Jefferson, and Madison 2002-10-08
From Lisa:
The longest-lived US presidents are John Adams(age90), Herbert Hoover (also90), and Harry Truman (88). Behind them are James Madison, Thomas Jefferson, and Richard Nixon. The lattter three men lived a total of 249 years, and their ages at the time of death form consecutive odd integers. For how long did Nixon, Jefferson, and Madison live?
Answered by Penny Nom.
Sole Mates Shoes 2002-08-19
From Robert:
Sole Mates Shoes has expenses of $9,592 per month. What must the store's total income be if it is to make a profit of 12%?
Answered by Penny Nom.
The average of two averages 2002-05-22
From RJ:
in a class with 22 students, the average garde on an exam was 68%, in another class with 32 students, the average grade on the same exam was 78%, what was the overall for the two classes? round your answers to the nearest whole number.
Answered by Leeanne Boehm.
Problem solving 2002-04-20
From Kathy:
  1. Zachary wanted to run the shore-to shore marathon next month, a 26 mile race from one side of the island where he lived to the other. He decided to work up to 26 miles by running five days a week for the next five weeks. Each day he'd run one mile longer than he did the day before, except for the first day of the week, when he'd run the same number of miles he ran on the last day of the previous week. He wanted his last two practice runs to be 26 and 27 miles long.

    How many miles would he have to run on his first practice run?

  2. A school just bought a new set of encyclopedias. The front and back covers are 1/8 inch thick, and the pages are 1/100 inch thick (in other words, there are 100 pages per inch). the 26 volume set has a total of 5,250 pages. If you assume there is no extra space left between books, then .........

    What length of bookshelf will the encyclopedias take up?

Answered by Penny Nom.
Number conversions and averages 2002-02-03
From A student:
A table has the measurements of 1.6m by 2m, how much material is needed to cover table? I converted to cm then multiplied but got an answer of 32000cm ,so I divide by 100 to get to metres - the answer was 320 which I know is wrong - please explain!!

Also I need to explain in my own words what an 'average' is and I am struggling.

Answered by Penny Nom.
Renee, Paulo and Peter 2001-11-18
From Sue:
Renee is 5 years older than Paulo. she is also 7 years older than Peter. The sum of their ages is 21. How old is each person.
Answered by Penny Nom.
Numbering pages 2001-11-15
From Lucy:
A printer uses 1008 digits to number the pages of a book. How many pages are there in the book?
Answered by Penny Nom.
15 mice in 4 cages 2001-10-08
From Chelsea:
How can you fit 15 mice into 4 cages with an odd number of mice in each cage?
Answered by Claude Tardif and Harley Weston.
David's wages 2001-09-24
From Kimberlee:
My math question is David earns $6.00 per hour plus $9.00 for every extra hour he works over 40 hours per week. If David earned $285.00 last week, how many extra hours did he work?
Answered by Penny Nom.
What did the girls score on average? 2001-07-20
From Rajesh:
The students of two schools were sitting the same test. The students attending the first school scored 74 on average; within this the average scores of the boys and the girls were 71 and 76, respectively. The corresponding scores in the other school were 84, 81 and 90, respectively. If the average score of all boys was 79, what did the girls score on average?
Answered by Penny Nom.
Monthly payments 2001-06-12
From Anthony:
This question is base on my interest. I would like to know the formula for calculating this example: If you borrow $10,000 from a bank with an APR of 11.7% to be paid off in 5 years, what is your monthly payment?
Answered by Penny Nom.
Solve for two variables 2001-02-25
From A student:
How do I solve for %1 and %2 in the following formula when T1, T2 and T3 are known? %1 and %2 are ratios of the same element, therefore %1 + %2 = 100%

(%1 x T1) + (%2 x T2) = T3

Answered by Penny Nom.
Winning percentages 2001-02-21
From Mike:



Answered by Harley Weston.
The ages of three daughters 2000-10-25
From Andrea:
An encyclopedia saleman call at a home. The woman who answers the door says she will buy something from him if he can give the ages of her three children. The first clue, she says, is the three ages multiplied together equal 36. he responds that he needs more infomration, so she says that the threee ages add up to the number of the bus that passed by (the prof did not give us this number) He thinks for a while and says he needs one more clue. So she says, my youngest child has red hair, and he is able to answer and make the sale. what are the ages of the three children? (hint: the salesman needed all three clues to get the answer).
Answered by Penny Nom.
Percents with mixed numbers 2000-06-04
From Julie:
How would you find the percent of 33 1/3 out of 90 by using fraction settup!I can do whole numbers but not mixed. This is how to do whole numbers say it was 33 of 90

33 x 90 = 2970
100 x 1 = 100
2970 divided by 100
the answer is 29.7

so how do you do it with a mixed number

Answered by Penny Nom.
What percent is one fraction of another fraction? 2000-04-29
From A student in grade 4:
What is the method for finding out what percent one fraction is of another fraction. For instance 4/5 is what percent of 1/9?
Answered by Penny Nom.
Folding a page 2000-03-01
From Krista Bischoff:
One corner of a page of width a is folded over and just reaches the opposite side. Express L, the length of the crease, in terms of x and a.

I can't get the picture to copy to this form so I guess I will have to try and describe the picture the best that I can. The top right hand corner is folded to the left side, almost half way down. The width of the paper is a ( the width of the bottom part which is not folded.) The creased side is L and the part shorter part of the folded area is x (the part that would have been the top right of the original piece.)

Answered by Chris Fisher.
Percentages 2000-01-09
From Nancy:

What is the best way for a parent to explain how one calculates percentages?

ie. Commission is $54268. Total Sales $403114.00 from that number how do you calculate the percentage of sales of various expenses.

Answered by Penny Nom.
Percent 1999-11-16
From Elaine Edwards:
Can you please tell me what is 75% of $495.00?
Answered by Penny Nom.
Predictions 1999-09-22
From Joesph Dana:
How do u find the results of an unbiased sample of 100 students that are shown on the table. For example the school has a total of 1,150 students prdict how many students would chose cereal(46) pancakes(15) eggs(20) and sandwich(19)
Answered by Haeley Weston.
Fractions, percents and decimals 1999-09-19
From Sue Farr:
My son is in 5th grade, and I can't seem to find any papers that have a simple explanation of how to convert decimals into fractions, percents into decimals, and vice-versa.
Answered by Harley Weston.
How many went to the game? 1999-09-09
From Lisa Schmidt:
If 3/4 more students went to the game than actually did go to the game, 25% of all students in the entire school would have gone. What fraction of students in the entire school went to the game?
Answered by Harley Weston.
Three Daughters 1999-05-18
From Norm Campbell:
I recently received a beat up copy of the three daughters question. I have only some of the question. It ends after the statement "the oldest one looks....... It does not finish. Is there any chance that someone can finish it off for me?
Answered by Rick Seaman and Harley Weston.
Percentages 1999-03-16
From Beth Barton:
If I have two figures and want to know the difference between them, in Percentage, how do I proceed with a calculation?

Example: 67,800 - 56,000 = 11,800
What percentage does this difference represent?
Answered by Jack LeSage.

Percentages 1998-07-10
From Adam:
I would like to know the basics of percentages. It is all rather confusing to me.I have excelled in math but want to be ready next year for more advanced math.

What is Percentages?
Answered by Penny Nom.

équations avec les ages 2006-11-06
From Ruffin:
Sébastien dit a Aurélie: vous avez 36 ans et j'ai deux 2 fois l'âge que vous aviez quand j'avais votre âge. Quel âge a Sébastien?
Answered by Claude Tardif.
Partages inégaux 2005-09-29
From Un eleve:
Alex et julie ont ensemble 4728 .- euro Si Alex donne 538.- euro à Julie, ce dernier aurait alors le triple de Julie. Quelle est la somme possédée de chacun?
Answered by Claude Tardif.



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