1999 AMC 8 Problem 7

Attempt Problem 7 of the 1999 AMC 8 below, then check your answer against the professionally curated solution 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.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

7.

The third exit on a highway is located at milepost 4040 and the tenth exit is at milepost 160.160. 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?
9090
100100
110110
120120
130130
Answer: E
Concepts:fraction
Small hint:
First find the distance between mileposts 4040 and 160160
Big hint:
Move 34\frac{3}{4} of that distance past milepost 4040
Solution:
There are 160−40=120160 - 40 = 120 miles between the third and tenth exits.
This means 34\frac{3}{4} of the way is at the 40+34⋅120=130 40 + \dfrac{3}{4} \cdot 120 = 130 milepost.
Thus, E is the correct answer.
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