Problem 7 · 1999 AMC 8
Medium
Fractions, Decimals & Percents
fraction-of
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?
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Answer: E — Milepost 130.
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Hint 1 of 2
"Three-fourths of the way" is a fraction of the gap between the exits, not three-fourths of 160. First find the gap.
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Hint 2 of 2
A fraction-of-the-way point = start + fraction × (gap). Don't forget to add it back onto the starting milepost.
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Approach: start + fraction of the gap (not fraction of the endpoint)
- The trap is multiplying ¾ × 160. The fraction applies to the gap: 160 − 40 = 120 miles, and ¾ of 120 is 90.
- Now add that distance onto where you started: 40 + 90 = 130.
- The reusable move: a "fraction of the way from A to B" point is A + fraction × (B − A). The exit numbers (third, tenth) are a distraction — only the mileposts matter.
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