Difference between revisions of "2017 AMC 10B Problems/Problem 12"
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| + | ==Video Solution== | ||
| + | https://youtu.be/KdhlT6DR_Do | ||
| + | |||
| + | ~savannahsolver | ||
{{AMC10 box|year=2017|ab=B|num-b=11|num-a=13}} | {{AMC10 box|year=2017|ab=B|num-b=11|num-a=13}} | ||
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Revision as of 19:13, 5 December 2020
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 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 ![\[15 : 12 = 5 : 4\]](http://latex.artofproblemsolving.com/2/1/e/21e9509e047a47a0dcffc35e8049a518e22ed0ad.png)
So the percentage of money saved is 
.
-Quadraticfunctions (edited by mydad)
Video Solution
~savannahsolver
| 2017 AMC 10B (Problems • Answer Key • Resources) | ||
| Preceded by Problem 11 |
Followed by Problem 13 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
| All AMC 10 Problems and Solutions | ||
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