2023 AMC 12B 第 1 题

Question

Jones 太太正在把橙汁倒入四个相同的杯子，给她的四个儿子喝。她把前三个杯子都倒满了，但橙汁用完时，第四个杯子只倒了

\tfrac13

满。Jones 太太需要从前三个杯子中的每一个倒出几分之一个杯子的橙汁到第四个杯子里，才能使四个杯子里的橙汁量都相同？

Mrs. Jones is pouring orange juice into four identical glasses for her four sons. She fills the first three glasses completely but runs out of juice when the fourth glass is only

\tfrac13

full. What fraction of a glass must Mrs. Jones pour from each of the first three glasses into the fourth glass so that all four glasses will have the same amount of juice?

\dfrac{1}{12}

\dfrac{1}{4}

\dfrac{1}{6}

\dfrac{1}{8}

\dfrac{2}{9}

答案：C

知识点：分数平均数

难度评级：890

小提示：

前三个满杯加上一个部分装满的杯子，橙汁总量是固定的

The three full glasses plus the partly full one hold a fixed total amount of juice

大提示：

总量是

3+\tfrac13

杯；除以

4

得到每杯最终的液面高度，再从

1

中减去它

The total is

3+\tfrac13

glasses; divide by

4

to get each glass’s final level, then subtract from

1

解答：

橙汁总量是

3+\tfrac13=\tfrac{10}{3}

杯。平均分成四份后，每个杯子应有

\tfrac{10}{3}\div 4=\tfrac{5}{6}

杯。因此前三个杯子中的每一个都必须倒出

1-\tfrac{5}{6}=\tfrac{1}{6}

。

因此，正确答案是 C。

The total juice is

3+\tfrac13=\tfrac{10}{3}

glasses. Split evenly, each glass should hold

\tfrac{10}{3}\div 4=\tfrac{5}{6}

of a glass. Each of the first three glasses must therefore give up

1-\tfrac{5}{6}=\tfrac{1}{6}.

Thus, the correct answer is C.

2023 AMC 12B 第 1 题

答案：C

难度评级：890

小提示：

大提示：

解答：

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