2022 AMC 10A Problem 4

Problem 4 of 25EasierAlgebra

In some countries, automobile fuel efficiency is measured in liters per

100

kilometers while other countries use miles per gallon. Suppose that

1

kilometer equals

m

miles, and

1

gallon equals

l

liters. Which of the following gives the fuel efficiency in liters per

100

kilometers for a car that gets

x

miles per gallon?

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Solution

A car that gets

x

miles per gallon uses

\frac{1}{x}

gallons per mile. Since

1

mile is

\frac{1}{m}

kilometers, this is

\frac{m}{x}

gallons per kilometer. Multiplying by

l

liters per gallon gives

\frac{lm}{x}

liters per kilometer, so for

100

kilometers the fuel used is

\frac{100lm}{x}

liters. Thus, E is the correct answer.