Problem 10 · 2012 Math Kangaroo
Medium
Algebra & Patterns
substitutionwork-backward
In addition to the weight of the basket, a single balloon can lift 80 kg. Two balloons can lift 180 kg in addition to the weight of the basket. How heavy is the basket?
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Answer: E — 20 kg
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Hint 1 of 2
Adding a second balloon adds another 80 kg of lift; compare the two situations.
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Hint 2 of 2
Find the basket weight by seeing how the totals jump from one balloon to two.
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Approach: compare one balloon vs two balloons
- Let the basket weigh b and one balloon's own lift be L. One balloon: L - b = 80.
- Two balloons: 2L - b = 180. Subtracting the first from the second gives L = 100.
- Then b = L - 80 = 100 - 80 = 20 kg. Check: 2(100) - 20 = 180.
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