AMC10 2022 A

AMC10 2022 A · Q4

AMC10 2022 A · Q4. It mainly tests Unit conversion.

In some countries, automobile fuel efficiency is measured in liters per $100$ kilometers while other countries use miles per gallon. Suppose that 1 kilometer equals $m$ miles, and $1$ gallon equals $l$ liters. Which of the following gives the fuel efficiency in liters per $100$ kilometers for a car that gets $x$ miles per gallon?

在一些国家，汽车燃油效率以每 $100$ 公里的升数衡量，而其他国家使用每加仑英里数。假设 $1$ 公里的英里数为 $m$，$1$ 加仑的升数为 $l$。以下哪项给出了每加仑 $x$ 英里的汽车每 $100$ 公里的燃油效率（升数）？

(A) \frac{x}{100lm} \frac{x}{100lm}

(B) \frac{xlm}{100} \frac{xlm}{100}

(D) \frac{100}{xlm} \frac{100}{xlm}

(E) \frac{100lm}{x} \frac{100lm}{x}

Answer

Correct choice: (E)

正确答案：（E）

Solution

The formula for fuel efficiency is \[\frac{\text{Distance}}{\text{Gas Consumption}}.\] Note that $1$ mile equals $\frac 1m$ kilometers. We have \[\frac{x\text{ miles}}{1\text{ gallon}} = \frac{\frac{x}{m}\text{ kilometers}}{l\text{ liters}} = \frac{1\text{ kilometer}}{\frac{lm}{x}\text{ liters}} = \frac{100\text{ kilometers}}{\frac{100lm}{x}\text{ liters}}.\] Therefore, the answer is $\boxed{\textbf{(E) } \frac{100lm}{x}}.$

燃油效率的公式是 \[\frac{\text{距离}}{\text{油耗}}.\] 注意 $1$ 英里等于 $\frac 1m$ 公里。我们有 \[\frac{x\text{ miles}}{1\text{ gallon}} = \frac{\frac{x}{m}\text{ kilometers}}{l\text{ liters}} = \frac{1\text{ kilometer}}{\frac{lm}{x}\text{ liters}} = \frac{100\text{ kilometers}}{\frac{100lm}{x}\text{ liters}}.\] 因此，答案是 $\boxed{\textbf{(E) } \frac{100lm}{x}}$。

Topics

AR.005 Unit conversion