1986 AMC 8 Problem 10

Attempt Problem 10 of the 1986 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 1986 AMC 8 solutions, or check the answer key.

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

10.

A picture 33 feet across is hung in the center of a wall that is 1919 feet wide. How many feet from the end of the wall is the nearest edge of the picture?
1121\dfrac12
88
9129\dfrac12
1616
2222
Answer: B
Concepts:symmetry
Small hint:
The picture is centered, so the two gaps on the sides are equal
Big hint:
Subtract the picture width from the wall width, then split the remainder between the two sides
Solution:
The picture leaves 19−3=1619 - 3 = 16 feet of wall, split equally into two gaps of 88 feet each. So the nearest edge of the picture is 88 feet from the end of the wall.
Thus, the correct answer is B .
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