Question

Joe 和 JoAnn 各买了 $12$ 盎司咖啡，装在 $16$ 盎司杯中。Joe 喝掉 $2$ 盎司咖啡后加入 $2$ 盎司奶油。JoAnn 先加入 $2$ 盎司奶油，充分搅拌后喝掉 $2$ 盎司。最终 Joe 咖啡中的奶油量与 JoAnn 咖啡中的奶油量之比是多少？

Joe and JoAnn each bought $12$ ounces of coffee in a $16$ -ounce cup. Joe drank $2$ ounces of his coffee and then added $2$ ounces of cream. JoAnn added $2$ ounces of cream, stirred the coffee well, and then drank $2$ ounces. What is the resulting ratio of the amount of cream in Joe's coffee to that in JoAnn's coffee?

$\dfrac{6}{7}$

$\dfrac{13}{14}$

$1$

$\dfrac{14}{13}$

$\dfrac{7}{6}$

答案：E

知识点：混合问题比与比例

难度评级：1340

解答：

Joe 加入 $2$ 盎司奶油后没有再喝，所以他有 $2$ 盎司奶油。

JoAnn 有 $12$ 盎司咖啡加 $2$ 盎司奶油，共 $14$ 盎司均匀混合液。喝掉 $2$ 盎司后，她保留了奶油的 $\tfrac{12}{14}=\tfrac67$ ，即 $\tfrac67\cdot2=\tfrac{12}{7}$ 盎司。

所求比为 $2\div\tfrac{12}{7}=\tfrac{7}{6}$ 。

所以正确答案是 E。

Joe adds $2$ ounces of cream and drinks nothing afterward, so he has $2$ ounces of cream.

JoAnn has $12$ ounces of coffee plus $2$ ounces of cream, making $14$ ounces of uniform mixture. After drinking $2$ ounces she keeps $\tfrac{12}{14}=\tfrac67$ of her cream, which is $\tfrac67\cdot2=\tfrac{12}{7}$ ounces.

The ratio is $2\div\tfrac{12}{7}=\tfrac{7}{6}.$

Thus, the correct answer is E.

2006 AMC 10B 第 13 题

答案：E

难度评级：1340

解答：

其他年份的第 13 题