2017 AMC 10 B
Complete problem set with solutions and individual problem pages
Elmer's new car gives better fuel efficiency. However, the new car uses diesel fuel, which is more expensive per liter than the gasoline the 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? (2017 AMC 10B Problem, Question#12)
- A.
- B.
- C.
- D.
- E.
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 .
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 .
You can find that the ratio of fuel used by the old car and the new car in a 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 .
