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Emily's Car

Source: 2022 AMC 10A #4

November 11, 2022
AMC 102022 AMC 10a2022 AMCAMCratesrate problemsalgebra

Problem Statement

In some countries, automobile fuel efficiency is measured in liters per 100100 kilometers while other countries use miles per gallon. Suppose that 11 kilometer equals mm miles, and 11 gallon equals ℓ\ell liters. Which of the following gives the fuel efficiency in liters per 100100 kilometers for a car that gets xx miles per gallon?
<spanclass=′latex−bold′>(A)</span>x100ℓm<spanclass=′latex−bold′>(B)</span>xℓm100<spanclass=′latex−bold′>(C)</span>ℓm100x<spanclass=′latex−bold′>(D)</span>100xℓm<spanclass=′latex−bold′>(E)</span>100ℓmx<span class='latex-bold'>(A) </span> \frac{x}{100\ell m} \qquad <span class='latex-bold'>(B) </span> \frac{x\ell m}{100} \qquad <span class='latex-bold'>(C) </span> \frac{\ell m}{100x} \qquad <span class='latex-bold'>(D) </span> \frac{100}{x\ell m} \qquad <span class='latex-bold'>(E) </span> \frac{100\ell m}{x}
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