Problem 10 · 1986 AJHSME
Medium
Geometry & Measurement
centering
A picture 3 feet across is hung in the center of a wall that is 19 feet wide. How many feet from the end of the wall is the nearest edge of the picture?
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Answer: B — 8.
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Hint 1 of 2
"Centered" is the whole secret: the wall left over after the picture is shared equally by the gap on the left and the gap on the right. So how much wall is left over, and how does it split?
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Hint 2 of 2
Find the leftover wall, then halve it — the two margins must be equal.
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Approach: leftover wall, split in half
- Because the picture is centered, the wall that isn't covered is split into two equal gaps, one on each side. So first find that leftover: 19 − 3 = 16 feet of empty wall.
- Split it evenly: 16 ÷ 2 = 8 feet from each end to the nearest edge of the picture.
- Sanity check: 8 + 3 (picture) + 8 = 19 ✓. Watch the trap — 9 1⁄2 is half of the *whole* wall (the center line), not the distance to the picture's edge.
Mark:
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