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2012 AMC 12A Problem 5

Problem 5 of 25EasierAlgebra

A fruit salad consists of blueberries, raspberries, grapes, and cherries. The fruit salad has a total of 280280 pieces of fruit. There are twice as many raspberries as blueberries, three times as many grapes as cherries, and four times as many cherries as raspberries. How many cherries are there in the fruit salad?

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Solution

Let bb be the number of blueberries. Then there are 2b2b raspberries, 4⋅2b=8b4 \cdot 2b = 8b cherries, and 3⋅8b=24b3 \cdot 8b = 24b grapes. The total is b+2b+8b+24b=35b=280,b + 2b + 8b + 24b = 35b = 280, so b=8b = 8 and there are 8b=648b = 64 cherries. Thus, the correct answer is D.

More practice

Concepts: ratio and proportion · system of equations

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.