Difference between revisions of "2022 AMC 10A Problems/Problem 4"
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Since it can be a bit odd to think of "liters per <math>100</math> km", this statement's numerical value is equivalent to <math>100</math> km per <math>1</math> liter: | Since it can be a bit odd to think of "liters per <math>100</math> km", this statement's numerical value is equivalent to <math>100</math> km per <math>1</math> liter: | ||
− | <math>1</math> km requires <math>l</math> liters, so the numerator is simply <math>l</math>. Since <math>l</math> liters is <math>1</math> gallon, and <math>x</math> miles is <math>1</math> gallon, we have <math>1 liter = \frac{x}{l}</math>. | + | <math>1</math> km requires <math>l</math> liters, so the numerator is simply <math>l</math>. Since <math>l</math> liters is <math>1</math> gallon, and <math>x</math> miles is <math>1</math> gallon, we have <math>1\text{ liter} = \frac{x}{l}</math>. |
Therefore, the requested expression is <cmath>100\cdot\frac{m}{(\frac{x}{l})} = \boxed{\textbf{(E) } \frac{100lm}{x}}.</cmath> | Therefore, the requested expression is <cmath>100\cdot\frac{m}{(\frac{x}{l})} = \boxed{\textbf{(E) } \frac{100lm}{x}}.</cmath> |
Revision as of 13:09, 14 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 1
The formula for fuel efficiency is
Note that
mile equals
kilometers. We have
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:
km requires
liters, so the numerator is simply
. Since
liters is
gallon, and
miles is
gallon, we have
.
Therefore, the requested expression is
-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 | |
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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