Problem 10 · 2015 Math Kangaroo
Medium
Algebra & Patterns
substitutionwork-backward
Andrea has 4 equally long strips of paper. When she glues two together with an overlap of 10 cm, she gets a strip 50 cm long. With the other two she wants to make a 56 cm long strip. How long must the overlap be?
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Answer: A — 4 cm
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Hint 1 of 2
Two strips glued together lose exactly one overlap from their combined length.
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Hint 2 of 2
First find the length of one strip from the 50 cm result, then use it for the 56 cm strip.
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Approach: find one strip length, then solve for the new overlap
- Two strips glued with a 10 cm overlap measure 50 cm, so the two full strips total 50 + 10 = 60 cm, meaning each strip is 30 cm.
- The other two strips also total 60 cm; gluing them to make 56 cm loses 60 − 56 = 4 cm to overlap.
- So the overlap must be 4 cm.
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