Skip to main content

2017 AMC 10B Problem 12

Problem 12 of 25IntermediateAlgebra

Elmer’s new car gets 50%50\% better fuel efficiency, measured in kilometers per liter, than his old car. However, his new car uses diesel fuel, which is 20%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?

Answer choices

Show solution

Solution

Let the old car’s fuel efficiency be MM kilometers per liter and let gasoline cost CC dollars per liter. The old car therefore costs CM\dfrac CM dollars per kilometer to fuel. The new car gets 1.5M1.5M kilometers per liter and its fuel costs 1.2C1.2C dollars per liter, so its fuel cost per kilometer is 1.2C1.5M=0.8CM.\dfrac{1.2C}{1.5M}=0.8\dfrac CM. The new fuel cost is 80%80\% of the old one, so Elmer saves 20%.20\%. Thus, the correct answer is A .

More practice

Concepts: rate · percentage

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.