Problem:
Elmer's new car gets better fuel efficiency, measured in kilometers per liter, than his old car. However, his new car uses diesel fuel, which is 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?
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Solution:
For Elmer's old car, let be the fuel efficiency in kilometers per liter, and let be the cost of fuel in dollars per liter. Then for his new car, the fuel efficiency is , and the cost of fuel is . The cost in dollars per kilometer for the old car is , and for the new car it is . Therefore, fuel for the long trip will cost less in Elmer's new car.
The problems on this page are the property of the MAA's American Mathematics Competitions