Question 1208119: Hi
Claudia and Agnes had some curry puffs. Claudia gave Agnes 1/4 of the number of curry puffs she had. Agnes gave Claudia 1/11 of the number she had. Both had the same number of curry puffs. If there were 240 curry puffs how many did each of them have.
Found 3 solutions by greenestamps, timofer, ikleyn:
Answer by greenestamps(13198)   (Show Source):
You can put this solution on YOUR website!
Notice that, the way the problem is stated, a sequence of events occurs, ending with each of them having the same number. So when at the end it asks "how many did each of them have", the answer is trivial -- (at the end) each of them had half of the total 240, or 120.
ANSWER (to the problem as stated): Each of them had 120
Clearly that is not the intent of the problem. The corrected (improved) statement of the problem is the following:
Claudia and Agnes had some curry puffs. Claudia gave Agnes 1/4 of the number of curry puffs she had.  Agnes gave Claudia 1/11 of the number she had.   Both had the same number of curry puffs. If there were 240 curry puffs how many did each of them have    .
Moving on to solve the problem as it was intended....
First a formal algebraic solution....
Let x = # Claudia started with
Then 240-x = # Agnes started with
First, Claudia gave Agnes 1/4 of hers. After that....
 = # Claudia had
 = # Agnes had
Then Agnes gave Claudia 1/11 of what she had. After that....
 = # Claudia had
 = # Agnes had
At that point, they had equal numbers:
Multiply everything by 11....
ANSWER: Claudia started with x=144; Agnes started with 240-x = 240-144 = 96
CHECK:
at the start: Claudia 144, Agnes 96
after Claudia gave 1/4 of hers to Agnes: Claudia 144-36 = 108; Agnes 96+36 = 132
after Agnes gave Claudia 1/11 of what she had: Agnes 132-12 = 120; Claudia 108+12 = 120
There are of course many other ways to set up the problem for solving using formal algebra.
But the problem can be solved informally with logical reasoning and simple arithmetic by working the problem backwards:
At the end, each of them had 120 -- half of the total 240.
Just before that, Agnes gave Claudia 1/11 of hers. That means the 120 Agnes had was 10/11 of what she had before giving some to Claudia. So the number Agnes had before giving some to Claudia was (11/10)(120) = 11*12 = 132. So the number Agnes gave to Claudia was 12, which means before Agnes gave those to Claudia the number Claudia had was 120-12 = 108.
Prior to that, Claudia gave Agnes 1/4 of hers, so the 108 Claudia had at that point was 3/4 of what she started with. So the number Claudia started with was (4/3)(108) = 4*36 = 144. And that means the number Agnes started with was 132-36 = 96.
ANSWERS: At the start, Claudia had 144 and Agnes had 96
Answer by timofer(104)  (Show Source):
You can put this solution on YOUR website! ~~~~~~~~~
Claudia and Agnes had some curry puffs. Claudia gave Agnes 1/4 of the number of curry puffs she had. Agnes gave Claudia 1/11 of the number she had. Both had the same number of curry puffs. If there were 240 curry puffs how many did each of them have.
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The giving and taking would not matter. The whole thing can just as well be stated this way.
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Claudia and Agnes had some curry puffs. Both had the same number of curry puffs. If there were 240 curry puffs how many did each of them have.
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Maybe the question should have been, "how many did each of them have at the beginning?"
Answer by ikleyn(52776)  (Show Source):
You can put this solution on YOUR website! .
Hi
Claudia and Agnes had some curry puffs. Claudia gave Agnes 1/4 of the number of curry puffs she had.
Agnes gave Claudia 1/11 of the number she had. Both had the same number of curry puffs.
If there were 240 curry puffs how many did each of them have.
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An extremely poorly written problem.
Total mess in the head of the author.
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