Luka is making lemonade to sell at a school fundraiser. His recipe requires $4$ times as much water as sugar and twice as much sugar as lemon juice. He uses $3$ cups of lemon juice. How many cups of water does he need?

A. 6

B. 8

C. 12

D. 18

E. 24

1. 2020 AMC 8 官方解析

The recipe requires twice as much sugar as lemon juice, so Luka needs $2 \cdot 3 = 6$ cups of sugar. The recipe requires $4$ times as much water as sugar, so Luka needs $4 \cdot 6 = 24$ cups of water.
该配方需要的糖量是柠檬汁的两倍，因此$Luka$需要$2 \cdot 3 = 6$杯糖。配方需要的水是糖的$4$倍，故$Luka$ 需要$4 \cdot 6 = 24$杯水。
The ratio of water to sugar to lemon juice in general is $8 : 2 : 1$. So if $3$ cups of lemon juice used, $8 \times 3 = 24$ cups of water would be needed.
该配方需要的水是糖的$4$倍，而需要的糖是柠檬汁的两倍。因此$Luka$ 需要的水是柠檬汁的$4 \cdot 2 = 8$倍。故她需要的水量是$8 \cdot 3 = 24$杯。