Problem 4 · 2014 Math Kangaroo
Easy
Algebra & Patterns
substitution
In three differently sized baskets there are 48 balls in total. Together the smallest and the biggest basket hold twice as many balls as the middle one. The smallest basket holds half as many balls as the middle one. How many balls are there in the biggest basket?
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Answer: C — 24
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Hint 1 of 2
Let the middle basket be your unit and write the others in terms of it.
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Hint 2 of 2
Three quantities add to 48 — turn the words into one equation in the middle amount.
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Approach: express all baskets through the middle one
- Let the middle basket hold m balls. The smallest holds m/2.
- Smallest + biggest = 2m, so biggest = 2m − m/2 = 3m/2.
- Total: m/2 + m + 3m/2 = 3m = 48, so m = 16.
- Biggest = 3m/2 = 24 balls.
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