Question

A fruit salad consists of blueberries, raspberries, grapes, and cherries. The fruit salad has a total of $280$ 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?

$8$

$16$

$25$

$64$

$96$

Answer: D

Concepts:ratio and proportion system of equations

Difficulty rating: 1040

Solution:

Let $b$ be the number of blueberries. Then there are $2b$ raspberries, $4 \cdot 2b = 8b$ cherries, and $3 \cdot 8b = 24b$ grapes.

The total is $b + 2b + 8b + 24b = 35b = 280,$ so $b = 8$ and there are $8b = 64$ cherries.

Thus, the correct answer is D.

2012 AMC 12A Problem 5

Answer: D

Difficulty rating: 1040

Solution:

Problem 5 in Other Years