AMC10 2018 A

AMC10 2018 A · Q2

AMC10 2018 A · Q2. It mainly tests Ratios & proportions.

Liliane has 50% more soda than Jacqueline, and Alice has 25% more soda than Jacqueline. What is the relationship between the amounts of soda that Liliane and Alice have?

Liliane 的苏打饮料比 Jacqueline 多 50%，Alice 的苏打饮料比 Jacqueline 多 25%。Liliane 和 Alice 的苏打饮料数量之间的关系是什么？

(A) Liliane has 20% more soda than Alice. Liliane 比 Alice 多 20% 的苏打水。

(B) Liliane has 25% more soda than Alice. Liliane 比 Alice 多 25% 的苏打水。

(D) Liliane has 75% more soda than Alice. Liliane 比 Alice 多 75% 的苏打水。

(E) Liliane has 100% more soda than Alice. Liliane 比 Alice 多 100% 的苏打水。

Answer

Correct choice: (A)

正确答案：（A）

Solution

Answer (A): Let $L$, $J$, and $A$ be the amounts of soda that Liliane, Jacqueline, and Alice have, respectively. The given information implies that $L=1.50J=\frac{3}{2}J$ and $A=1.25J=\frac{5}{4}J$, and hence $J=\frac{4}{5}A$. Then \[ L=\frac{3}{2}\cdot\frac{4}{5}A=\frac{6}{5}A=1.20A, \] so Liliane has $20\%$ more soda than Alice.

答案（A）：设 $L$、$J$、$A$ 分别表示 Liliane、Jacqueline 和 Alice 拥有的汽水量。由题意可得 $L=1.50J=\frac{3}{2}J$，且 $A=1.25J=\frac{5}{4}J$，因此 $J=\frac{4}{5}A$。于是 \[ L=\frac{3}{2}\cdot\frac{4}{5}A=\frac{6}{5}A=1.20A, \] 所以 Liliane 比 Alice 多 $20\%$ 的汽水。

Topics

AR.004 Ratios & proportions