Question

一份水果沙拉由蓝莓、覆盆子、葡萄和樱桃组成。水果沙拉中共有 $280$ 块水果。覆盆子的数量是蓝莓的两倍，葡萄的数量是樱桃的三倍，樱桃的数量是覆盆子的四倍。水果沙拉中有多少颗樱桃？

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?

$8$

$16$

$25$

$64$

$96$

答案：D

知识点：比与比例方程组

难度评级：1040

小提示：

用蓝莓的数量表示每一种水果的数量

Express every count in terms of the number of blueberries

大提示：

若有 $b$ 颗蓝莓，则有 $2b$ 颗覆盆子， $8b$ 颗樱桃， $24b$ 颗葡萄

With $b$ blueberries there are $2b$ raspberries, $8b$ cherries, and $24b$ grapes

解答：

设蓝莓有 $b$ 颗。则覆盆子有 $2b$ 颗，樱桃有 $4 \cdot 2b = 8b$ 颗，葡萄有 $3 \cdot 8b = 24b$ 颗。

总数为 $b + 2b + 8b + 24b = 35b = 280$ ，所以 $b = 8$ ，樱桃有 $8b = 64$ 颗。

因此，正确答案是 D。

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 第 5 题

答案：D

难度评级：1040

小提示：

大提示：

解答：

其他年份的第 5 题