AMC8 2009

AMC8 2009 · Q15

AMC8 2009 · Q15. It mainly tests Ratios & proportions, Arithmetic misc.

A recipe that makes 5 servings of hot chocolate requires 2 squares of chocolate, $\frac{1}{4}$ cup sugar, 1 cup water and 4 cups milk. Jordan has 5 squares of chocolate, 2 cups of sugar, lots of water and 7 cups of milk. If she maintains the same ratio of ingredients, what is the greatest number of servings of hot chocolate she can make?

一份制作 5 份热巧克力的配方需要 2 块巧克力、$\frac{1}{4}$ 杯糖、1 杯水和 4 杯牛奶。乔丹有 5 块巧克力、2 杯糖、充足的水和 7 杯牛奶。如果她保持相同的配方比例，她最多能做多少份热巧克力？

(A) $5\frac{1}{8}$ $5\frac{1}{8}$

(B) $6\frac{1}{4}$ $6\frac{1}{4}$

(D) $8\frac{3}{4}$ $8\frac{3}{4}$

(E) $9\frac{7}{8}$ $9\frac{7}{8}$

Answer

Correct choice: (D)

正确答案：（D）

Solution

Answer (D): Jordan has 5 squares of chocolate, which is $2\frac{1}{2}$ times the amount the recipe calls for. She has $2 \div \frac{1}{4} = 8$ times the amount of sugar and $\frac{7}{4} = 1\frac{3}{4}$ times the amount of milk necessary to make the recipe. So the amount of milk limits the number of servings. Jordan cannot make more than $5\left(1\frac{3}{4}\right)=5\left(\frac{7}{4}\right)=\frac{35}{4}=8\frac{3}{4}$ servings of hot chocolate.

答案（D）：Jordan 有 5 块巧克力，这是食谱所需量的 $2\frac{1}{2}$ 倍。她的糖有 $2 \div \frac{1}{4} = 8$ 倍于做该食谱所需的量，而牛奶有 $\frac{7}{4} = 1\frac{3}{4}$ 倍于做该食谱所需的量。因此，牛奶的数量限制了可制作的份数。Jordan 最多只能做 $5\left(1\frac{3}{4}\right)=5\left(\frac{7}{4}\right)=\frac{35}{4}=8\frac{3}{4}$ 份热巧克力。

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