Difference between revisions of "2022 AMC 10A Problems/Problem 4"
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==Problem== | ==Problem== | ||
| − | In some countries, automobile fuel efficiency is measured in liters per <math>100</math> kilometers while other countries use miles per gallon. Suppose that 1 kilometer equals <math>m</math> miles, and <math>1</math> gallon equals <math>l</math> liters. Which of the following gives the fuel efficiency in liters per <math>100</math> kilometers for a car that gets <math>x</math> miles per gallon | + | In some countries, automobile fuel efficiency is measured in liters per <math>100</math> kilometers while other countries use miles per gallon. Suppose that 1 kilometer equals <math>m</math> miles, and <math>1</math> gallon equals <math>l</math> liters. Which of the following gives the fuel efficiency in liters per <math>100</math> kilometers for a car that gets <math>x</math> miles per gallon? |
<math>\textbf{(A) } \frac{x}{100lm} \qquad \textbf{(B) } \frac{xlm}{100} \qquad \textbf{(C) } \frac{lm}{100x} \qquad \textbf{(D) } \frac{100}{xlm} \qquad \textbf{(E) } \frac{100lm}{x}</math> | <math>\textbf{(A) } \frac{x}{100lm} \qquad \textbf{(B) } \frac{xlm}{100} \qquad \textbf{(C) } \frac{lm}{100x} \qquad \textbf{(D) } \frac{100}{xlm} \qquad \textbf{(E) } \frac{100lm}{x}</math> | ||
Revision as of 19:22, 11 November 2022
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
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
See Also
| 2022 AMC 10A (Problems • Answer Key • Resources) | ||
| Preceded by Problem 3 |
Followed by Problem 5 | |
| 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 | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
