2022 AMC 10A Problems/Problem 4
Problem
In some countries, automobile fuel efficiency is measured in liters per 
kilometers while other countries use miles per gallon. Suppose that 1 kilometer equals 
miles, and 
gallon equals 
liters. Which of the following gives the fuel efficiency in liters per kilometers for a car that gets 
miles per gallon?
Solution 1
The formula for fuel efficiency is ![\[\frac{\text{Distance}}{\text{Gas Consumption}}.\]](http://latex.artofproblemsolving.com/9/0/e/90eeec553fea9ce3012153b8582c2d9f6a593332.png)
Note that mile equals 
kilometers. We have ![\[\frac{x\text{ miles}}{1\text{ gallon}} = \frac{\frac{x}{m}\text{ kilometers}}{l\text{ liters}} = \frac{1\text{ kilometer}}{\frac{lm}{x}\text{ liters}} = \frac{100\text{ kilometers}}{\frac{100lm}{x}\text{ liters}}.\]](http://latex.artofproblemsolving.com/6/0/c/60c6bc79b632eb92edc1ac2b7389e21da8beb47b.png)
Therefore, the answer is 
~MRENTHUSIASM
Solution 2
Since it can be a bit odd to think of "liters per km", this statement's numerical value is equivalent to km per liter:
requires 
so the numerator is simply . Since liters is gallon, and miles is gallon, we have 
.
Therefore, the requested expression is ![\[100\cdot\frac{m}{(\frac{x}{l})} = \frac{100lm}{x} \rightarrow \boxed{\textbf{(E) } \frac{100lm}{x}}.\]](http://latex.artofproblemsolving.com/e/4/e/e4ee1069494e72df91c7ecccb8e3578f17da353b.png)
-Benedict T (countmath1)
Video Solution 1 (Quick and Easy)
~Education, the Study of Everything
See Also
| 2022 AMC 10A (Problems • Answer Key • Resources) | ||
| Preceded by Problem 3 |
Followed by Problem 5 | |
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| All AMC 10 Problems and Solutions | ||
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