Question 1043733: How would I go about solving problems like this?
Carol shared graph paper with 3 friends. She game 1/4 to Willy, 1/3 to Sara and then 1/6 to to Marcy. Carol has 30 sheets remaining. How many did she start with?
The answer in the back of the book say 72 is the answer but I get 59 every time.
Found 2 solutions by stanbon, Boreal:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! How would I go about solving problems like this?
Carol shared graph paper with 3 friends. She game 1/4 to Willy, then
she gave (1/3) of the remaining to Sara and then she
gave 1/6 of the remaining to Marcy.
Carol has 30 sheets remaining. How many did she start with?
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Start:: x sheets
(1/4)x to Willy:: (3/4)x remaining
(1/3)(3/4)x to Sara = (1/4)x to Sara:: (1/2)x remaining
(1/6)(1/2)x) to Marcy = (1/12)x to Marcy:: (1/2 - 1/12)x = (5/12)x remaining
------
Equation:
(5/12)x = 30
x = 72
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Cheers,
Stan H.
Answer by Boreal(15235)  (Show Source):
You can put this solution on YOUR website! x is what she has.
(1/4)x is to Willy
(1/3)x to Sara
(1/6)x to Marcy
What is important in this question is that the wording is not quite accurate.
She gave (1/4) to Willy, then with what was left, she gave (1/3) to Sara, and with what was left (1/6) to Marcy. She has 30 sheets left. If this wording isn't used, the answer is 120.
She had (3/4) left after Willy, and (3/4)(1/3)=(1/4), so now she has (3/4)-(1/4) or 1/2 after Sara.
She gave Marcy (1/6) of (1/2) or (1/12) of her paper.
She started with (1/2), so after Marcy she had (1/2)-(1/12)=(5/12)x
That is equal to 30.
(5/12)x=30
Multiply both sides by the reciprocal (12/5)
30*(12/5)=72.
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