AMC12 2023 B

AMC12 2023 B · Q1

AMC12 2023 B · Q1. It mainly tests Fractions, Averages (mean).

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 $\frac{1}{3}$ 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?

琼斯太太正在为她的四个儿子往四个相同的玻璃杯里倒橙汁。她把前三个玻璃杯完全装满，但当第四个玻璃杯只装满 $\frac{1}{3}$ 时汁用完了。琼斯太太必须从前三个玻璃杯的每个杯子里倒出多少杯的量到第四个玻璃杯里，使得四个玻璃杯都有相同量的汁？

(A) \frac{1}{12} \frac{1}{12}

(B) \frac{1}{4} \frac{1}{4}

(D) \frac{1}{8} \frac{1}{8}

(E) \frac{2}{9} \frac{2}{9}

Answer

Correct choice: (C)

正确答案：（C）

Solution

The first three glasses each have a full glass. Let's assume that each glass has "1 unit" of juice. It won't matter exactly how much juice everyone has because we're dealing with ratios, and that wouldn't affect our answer. The fourth glass has a glass that is one third. So the total amount of juice will be $1+1+1+\dfrac{1}{3} = \dfrac{10}{3}$. If we divide the total amount of juice by 4, we get $\dfrac{5}{6}$, which should be the amount of juice in each glass. This means that each of the first three glasses will have to contribute $1 - \dfrac{5}{6} = \boxed{\textbf{(C) }\dfrac16}$ to the fourth glass.

前三个玻璃杯每个都有满杯。假设每个玻璃杯有“1单位”的汁。因为我们处理的是比例，无论每个人具体有多少汁都不会影响答案。第四个玻璃杯有 $\frac{1}{3}$ 杯。所以总汁量是 $1+1+1+\dfrac{1}{3} = \dfrac{10}{3}$。如果我们将总汁量除以4，得到 $\dfrac{5}{6}$，这应该是每个玻璃杯的汁量。这意味着前三个玻璃杯中的每个都需要贡献 $1 - \dfrac{5}{6} = \boxed{\textbf{(C) }\dfrac16}$ 到第四个玻璃杯。

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