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Help Needed

by sanalnnair » Mon Sep 13, 2010 11:44 pm
1. A fruit salad contains 2/3 blueberries and the rest raspberries. Chen loves raspberries, so she added 12 quarts of raspberries to the salad. If the mixture is now 5/7 raspberries, how many quarts of fruit salad were there to begin with?
(A) 9
(B) 12
(C) 15
(D) 21
(E) 25

Ans [spoiler](A)- 9[/spoiler]

Source - Princeton Review


I had made a table of Blueberries, Raspberries and then solved the question. Since there are 2/3 blueberries initially, then the number of raspberries would be 1/3.

We are given the total mixture contains 5/7 raspberries, hence the blueberries would be 2/7.

So since we add 12 to the initial mixture, the answer should be a multiple of 7. And then I got the answer as [spoiler]9. (A).[/spoiler]


Is there any other way of approaching this problem??
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by limestone » Tue Sep 14, 2010 1:59 am
Well, you have a great short cut to the problem. And this is my approach:

Since the proportion of blueberries is unchanged, then 2/3 of the original salad ( the proportion of blueberries in the original salad) = (1 - 5/7) of the already-added salad ( the proportion of blueberries in the new salad)

or 2/3 of the original one = 2/7 of the new one.
The original one ( or 3/3) = 3/7 of the new one
so the 12 added quarts equals:1- 3/7 = 4/7 of the new one
1/7 of the new one = 1/3 of the original = 12/4 = 3
So the new one contains : 3 x 7 = 21 quarts
The original contains: 3 x 3 = 9

The answer is A.
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