Question

Joe 和 JoAnn 各自在 $16$ 盎司杯中买了 $12$ 盎司咖啡。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，充分搅拌后再喝掉 $2$ 盎司。最后 Joe 的咖啡中奶油量与 JoAnn 的咖啡中奶油量之比是多少？

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：1510

小提示：

Joe 是喝完后才加奶油，所以他的 $2$ 盎司奶油全部留下

Joe adds cream after drinking, so all $2$ ounces of his cream remain

大提示：

JoAnn 从充分混合的 $14$ 盎司饮料中喝掉一部分，奶油按比例减少

JoAnn drinks from a well-mixed $14$ -ounce cup, removing cream in proportion

解答：

Joe 最后加入奶油，所以杯中保留了全部 $2$ 盎司奶油。

JoAnn 的杯中有 $14$ 盎司混合物，其中含 $2$ 盎司奶油。喝掉 $2$ 盎司会按比例移走 $\tfrac{2}{14}$ 的所有成分，剩下的奶油为 $2 \cdot \frac{12}{14} = \frac{12}{7}$ 盎司。

比值为 $\frac{2}{\,\frac{12}{7}\,} = \frac{14}{12} = \frac{7}{6}\text{。}$

因此，正确答案是 E。

Joe adds the cream last, so his cup holds all $2$ ounces of cream.

JoAnn’s cup has $14$ ounces of mixture containing $2$ ounces of cream. Drinking $2$ ounces removes a fraction $\tfrac{2}{14}$ of everything, leaving $2 \cdot \frac{12}{14} = \frac{12}{7}$ ounces of cream.

The ratio is $\frac{2}{\,\frac{12}{7}\,} = \frac{14}{12} = \frac{7}{6}.$

Thus, the correct answer is E.

2006 AMC 12B 第 11 题

答案：E

难度评级：1510

小提示：

大提示：

解答：

其他年份的第 11 题