2002 AMC 12A 第 10 题

Question

Sarah 将四盎司咖啡倒入一个八盎司杯中，又将四盎司奶油倒入另一个同样大小的杯子。她把第一杯中一半的咖啡倒入第二杯，充分搅拌后，再把第二杯中一半的液体倒回第一杯。现在第一杯中的液体有几分之几是奶油？

Sarah pours four ounces of coffee into an eight-ounce cup and four ounces of cream into a second cup of the same size. She then transfers half the coffee from the first cup to the second and, after stirring thoroughly, transfers half the liquid in the second cup back to the first. What fraction of the liquid in the first cup is now cream?

\dfrac{1}{4}

\dfrac{1}{3}

\dfrac{3}{8}

\dfrac{2}{5}

\dfrac{1}{2}

答案：D

知识点：混合问题分数

难度评级：1440

小提示：

第一次转移后，杯

2

有

2

oz 咖啡和

4

oz 奶油。

After the first transfer, cup

2

holds

2

oz coffee and

4

oz cream

大提示：

杯

2

倒回一半时，会按相同比例转移咖啡和奶油；求杯

1

中的奶油量。

Transferring back half of cup

2

moves its coffee and cream in equal proportion; find the cream in cup

1

解答：

倒出一半咖啡后，杯

1

有

2

oz 咖啡；杯

2

有

2

oz 咖啡和

4

oz 奶油，共

6

oz。

杯

2

倒回一半，会转移

1

oz 咖啡和

2

oz 奶油。于是杯

1

有

2 + 1 = 3

oz 咖啡和

2

oz 奶油。

奶油所占比例为

\dfrac{2}{2+3} = \dfrac{2}{5}

。

因此，正确答案是 D。

After transferring half the coffee, cup

1

has

2

oz coffee and cup

2

has

2

oz coffee and

4

oz cream, a total of

6

oz.

Transferring half of cup

2

back moves

1

oz coffee and

2

oz cream. Cup

1

then holds

2 + 1 = 3

oz coffee and

2

oz cream.

The fraction that is cream is

\dfrac{2}{2+3} = \dfrac{2}{5}.

Thus, the correct answer is D.

2002 AMC 12A 第 10 题

答案：D

难度评级：1440

小提示：

大提示：

解答：

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