Difference between revisions of "1986 AHSME Problems/Problem 14"

Problem

Suppose hops, skips and jumps are specific units of length. If $b$ hops equals $c$ skips, $d$ jumps equals $e$ hops, and $f$ jumps equals $g$ meters, then one meter equals how many skips?

$\textbf{(A)}\ \frac{bdg}{cef}\qquad \textbf{(B)}\ \frac{cdf}{beg}\qquad \textbf{(C)}\ \frac{cdg}{bef}\qquad \textbf{(D)}\ \frac{cef}{bdg}\qquad \textbf{(E)}\ \frac{ceg}{bdf}$

Solution

$1$ metre equals $\frac{f}{g}$ jumps, which is $\frac{f}{g} \frac{e}{d}$ hops, and then $\frac{f}{g} \frac{e}{d} \frac{c}{b}$ skips, which becomes $\frac{cef}{bdg}$, i.e. answer $\boxed{D}$.