Problem:
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?
Answer Choices:
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Solution:
For each blueberry in the fruit salad there are 2 raspberries, 8 cherries, and 24 grapes. Thus there are pieces of fruit for each blueberry. Because , it follows that there are a total of 8 blueberries, raspberries, cherries, and grapes in the fruit salad. Thus there are cherries.
The problems on this page are the property of the MAA's American Mathematics Competitions