AMC10 2006 B

AMC10 2006 B · Q13

AMC10 2006 B · Q13. It mainly tests Fractions, Mixture / concentration.

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?

Joe 和 JoAnn 各买了 12 盎司咖啡，装在 16 盎司的杯子里。Joe 喝了 2 盎司咖啡后加了 2 盎司奶油。JoAnn 先加了 2 盎司奶油，充分搅拌后喝了 2 盎司。Joe 的咖啡中奶油量与 JoAnn 的咖啡中奶油量的比值为多少？

(A) $\frac{6}{7}$ $\frac{6}{7}$

(B) $\frac{13}{14}$ $\frac{13}{14}$

(D) $\frac{14}{13}$ $\frac{14}{13}$

(E) $\frac{7}{6}$ $\frac{7}{6}$

Answer

Correct choice: (E)

正确答案：（E）

Solution

Joe has 2 ounces of cream in his cup. JoAnn has drunk 2 ounces of the 14 ounces of coffee-cream mixture in her cup, so she has only $12/14 = 6/7$ of her 2 ounces of cream in her cup. Therefore the ratio of the amount of cream in Joe's coffee to that in JoAnn's coffee is $$\frac{2}{\frac{6}{7} \cdot 2} = \frac{7}{6}.$$

Joe 的杯中有 2 盎司奶油。JoAnn 喝了 14 盎司咖啡-奶油混合物中的 2 盎司，因此她杯中剩余的奶油量是其 2 盎司奶油的 $12/14 = 6/7$。因此 Joe 的咖啡中奶油量与 JoAnn 的比值为 $$\frac{2}{\frac{6}{7} \cdot 2} = \frac{7}{6}。$$

Topics