1986 AMC 12 第 14 题

Question

假设“跃步”“跨步”和“跳步”是特定的长度单位。若

b

个跃步等于

c

个跨步，

d

个跳步等于

e

个跃步，且

f

个跳步等于

g

米，那么一米等于多少个跨步？

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}

将每个等式化为一个单位的换算关系

Turn each equality into a conversion factor for one unit

依次将米换算为跳步、将跳步换算为跃步、再将跃步换算为跨步

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

由三个关系可得

\begin{aligned} 1\text{ 米}&=\frac fg\text{ 个跳步},\\ 1\text{ 个跳步}&=\frac ed\text{ 个跃步},\\ 1\text{ 个跃步}&=\frac cb\text{ 个跨步}\text{。} \end{aligned}

将换算因子相乘，得到

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

个跨步。

所以正确答案是 D。

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.

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