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berries

Problem Solving — algebra and arithmetic
Expert replies
by rupsk » Sun Nov 13, 2011 3:11 pm
Danny has boxes colored either red or blue. In each blue box there is a fixed number of blueberries. In each red box there is a fixed number of strawberries. If Danny disposed of one blue box for one additional red box, the total number of berries (of both kinds) would increase by 25, and the difference between the total number of strawberries and the total number of blueberries would increase by 95. Each blue box contains how many blueberries?

(1)35
(2)40
3)45
4)50
(5)60
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Source: — Quantitative Reasoning |

by neelgandham » Sun Nov 13, 2011 3:57 pm
Let R be the number of Strawberry boxes.
Let R1 be the number of Strawberries per box.
Total number of Strawberries = R*R1

Let B be the number of Blueberry boxes.
Let B1 be the number of Blueberries per box.
Total number of Strawberries = B*B1
If Danny disposed of one blue box for one additional red box, the total number of berries (of both kinds) would increase by 25
Total number of fruits = R*R1 + B*B1
Total number of berries after the exchange = R*R1 + B*B1 + R1 - B1
Implies R1-B1 =25
difference between the total number of strawberries and the total number of blueberries would increase by 95. Each blue box contains how many blueberries
Difference between the total number of strawberries and the total number of blueberries before the exchange = R*R1 - B*B1

Difference between the total number of strawberries and the total number of blueberries after the exchange = R*R1 + R1 - (B*B1 - B1)

From the quoted statement above, R*R1 + R1 - (B*B1 - B1) - R*R1 - B*B1 = 95
Implies R1 + B1 = 95

R1-B1 =25 and R1+B1 = 95
B1 = (95-25)/2 = 35

IMO A
Anil Gandham
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