1986 AMC 12 Problem 14

Question

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?

\frac{bdg}{cef}

\frac{cdf}{beg}

\frac{cdg}{bef}

\frac{cef}{bdg}

\frac{ceg}{bdf}

Turn each equality into a conversion factor for one unit

Convert meters to jumps, jumps to hops, and hops to skips in that order

From the three relations,

\begin{aligned} 1\text{ meter}&=\frac fg\text{ jumps},\\ 1\text{ jump}&=\frac ed\text{ hops},\\ 1\text{ hop}&=\frac cb\text{ skips}. \end{aligned}

Multiplying the conversion factors gives

\frac fg\cdot\frac ed\cdot\frac cb=\frac{cef}{bdg}

skips.

Thus the correct answer is D.

Problem 14 in other years