2006 AMC 12B 第 11 题

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：

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