AMC10 2017 B

AMC10 2017 B · Q12

AMC10 2017 B · Q12. It mainly tests Rates (speed).

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?

Elmer的新车燃油效率比旧车高50%，以千米每升计。然而，新车使用柴油，每升价格比旧车用的汽油贵20%。Elmer用新车代替旧车进行长途旅行，能节省多少钱的百分比？

(A) 20% 20%

(B) $26 \frac{2}{3}\%$ $26 \frac{2}{3}\%$

(D) $33 \frac{1}{3}\%$ $33 \frac{1}{3}\%$

(E) $41 \frac{2}{3}\%$ $41 \frac{2}{3}\%$

Answer

Correct choice: (A)

正确答案：（A）

Solution

For Elmer’s old car, let M be the fuel efficiency in kilometers per liter, and let C be the cost of fuel in dollars per liter. Then for his new car, the fuel efficiency is 1.5M, and the cost of fuel is 1.2C. The cost in dollars per kilometer for the old car is C/M, and for the new car it is 1.2C / 1.5M = 0.8 (C/M). Therefore, fuel for the long trip will cost 20% less in Elmer’s new car.

对于Elmer的旧车，让M为燃油效率（千米每升），C为燃料成本（美元每升）。则新车的燃油效率为1.5M，燃料成本为1.2C。旧车的每千米成本为C/M，新车为1.2C / 1.5M = 0.8 (C/M)。因此，长途旅行的燃料在新车上便宜20%。

Topics

AR.007 Rates (speed)