Problem 12 · 2012 Math Kangaroo
Medium
Algebra & Patterns
substitution
When Adam stands on a table and Mike on the floor, Adam is 80 cm taller than Mike. When Mike stands on the table and Adam on the floor, Mike is one metre taller than Adam. How high is the table?
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Answer: C — 90 cm
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Hint 1 of 2
Write the two situations as equations using Adam's height, Mike's height, and the table.
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Hint 2 of 2
Add the two equations — the heights cancel and leave twice the table height.
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Approach: set up two equations and add them
- With Adam on the table: (Adam + table) − Mike = 80.
- With Mike on the table: (Mike + table) − Adam = 100.
- Add the two equations: the heights cancel, giving 2 × table = 180, so the table is 90 cm (C).
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