2017 AMC 10B Problems/Problem 12

Problem

Elmer's new car gives percent 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 used. By what percent will Elmer save money if he uses his new car instead of his old car for a long trip?

Solution 1

Suppose that his old car runs at km per liter. Then his new car runs at km per liter, or km per of a liter. Let the cost of the old car's fuel be , so the trip in the old car takes dollars, while the trip in the new car takes . He saves .

Solution 2

Because they do not give you a given amount of distance, we'll just make that distance miles. Then, we find that the new car will use . The old car will use . Thus the answer is .

-Lcz

Solution 3

You can find that the ratio of fuel used by the old car and the new car for the same amount of distance is , and the ratio between the fuel price of these two cars is . Therefore, by multiplying these two ratios, we get that the costs of using these two cars is So the percentage of money saved is .

-Quadraticfunctions (edited by mydad)

Video Solution

https://youtu.be/KdhlT6DR_Do

~savannahsolver

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I don't see how the problem implies that it runs 1.5 times the distance, couldn't it also mean that it takes 50% less fuel to go the same distance?

See Also

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.