AMC10 2002 A

AMC10 2002 A · Q17

AMC10 2002 A · Q17. It mainly tests Fractions, Mixture / concentration.

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?

Sarah 将四盎司咖啡倒入一个八盎司的杯子中，并将四盎司奶油倒入另一个同等大小的杯子中。然后她将第一杯中一半的咖啡转移到第二杯中，彻底搅拌后，将第二杯中一半的液体转移回第一杯。第一杯中的液体现在有多少是奶油？

(A) 1/4 1/4

(B) 1/3 1/3

(D) 2/5 2/5

(E) 1/2 1/2

Answer

Correct choice: (D)

正确答案：（D）

Solution

(D) After the first transfer, the first cup contains two ounces of coffee, and the second cup contains two ounces of coffee and four ounces of cream. After the second transfer, the first cup contains $2 + (1/2)(2) = 3$ ounces of coffee and $(1/2)(4) = 2$ ounces of cream. Therefore, the fraction of the liquid in the first cup that is cream is $2/(2 + 3) = 2/5$.

（D）第一次转移后，第一个杯子里有2盎司咖啡，第二个杯子里有2盎司咖啡和4盎司奶油。第二次转移后，第一个杯子里有 $2 + (1/2)(2) = 3$ 盎司咖啡，且有 $(1/2)(4) = 2$ 盎司奶油。因此，第一个杯子中液体里奶油所占的比例为 $2/(2 + 3) = 2/5$。

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