1999 AMC 8 Problem 7

Below is the professionally curated solution for Problem 7 of the 1999 AMC 8, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1999 AMC 8 solutions, or check the answer key.

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Concepts:fraction

Difficulty rating: 900

The third exit on a highway is located at milepost $40$ and the tenth exit is at milepost $160.$ There is a service center on the highway located three-fourths of the way from the third exit to the tenth exit. At what milepost would you expect to find this service center?

$90$

$100$

$110$

$120$

$130$

Solution:

There are $160 - 40 = 120$ mileposts between the third and tenth exits.

This means $\frac{3}{4}$ of the way is at the $40 + \dfrac{3}{4} \cdot 120 = 130$ milepost.

Thus, E is the correct answer.

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