Question

Elmer 的新车燃油效率（以每升行驶千米数衡量）比旧车高 $50\%$ 。不过新车使用柴油，柴油每升价格比旧车使用的汽油贵 $20\%$ 。如果 Elmer 长途旅行时使用新车而不是旧车，他会省下百分之多少的钱？

Elmer’s new car gets $50\%$ better fuel efficiency, measured in kilometers per liter, than his old car. However, his new car uses diesel fuel, which is $20\%$ more expensive per liter than the gasoline his old car uses. By what percent will Elmer save money if he uses his new car instead of his old car for a long trip?

$20\%$

$26\tfrac23\%$

$27\tfrac79\%$

$33\tfrac13\%$

$41\tfrac23\%$

答案：A

知识点：速率百分数

难度评级：1280

小提示：

比较每千米成本，而不是每升成本。

Compare cost per kilometer, not cost per liter

大提示：

新燃料用的升数更少，但每升更贵。

New fuel uses fewer liters but each liter costs more

解答：

设旧车的燃油效率为每升 $M$ 千米，汽油价格为每升 $C$ 美元。于是旧车每千米的燃油费用为 $\dfrac CM$ 美元。

新车每升可行驶 $1.5M$ 千米，而它所用燃料的价格为每升 $1.2C$ 美元，所以新车每千米的燃油费用为 $\dfrac{1.2C}{1.5M}=0.8\dfrac CM\text{。}$

新车的燃油费用是旧车的 $80\%$ ，所以 Elmer 节省了 $20\%$ 。

所以正确答案是 A。

Let the old car’s fuel efficiency be $M$ kilometers per liter and let gasoline cost $C$ dollars per liter. The old car therefore costs $\dfrac CM$ dollars per kilometer to fuel.

The new car gets $1.5M$ kilometers per liter and its fuel costs $1.2C$ dollars per liter, so its fuel cost per kilometer is $\dfrac{1.2C}{1.5M}=0.8\dfrac CM.$

The new fuel cost is $80\%$ of the old one, so Elmer saves $20\%.$

Thus, the correct answer is A .

2017 AMC 10B 第 12 题

答案：A

难度评级：1280

小提示：

大提示：

解答：

其他年份的第 12 题