Problem 13 · 2019 Math Kangaroo
Medium
Arithmetic & Operations
divisionwork-backward
Sara has 16 blue marbles. She can swap her marbles in the following way: for 3 blue marbles she gets 1 red marble, and for 2 red marbles she gets 5 green marbles. What is the maximum number of green marbles she can get?
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Answer: B — 10
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Hint 1 of 2
First turn as many blue marbles as possible into red ones, then trade reds for greens.
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Hint 2 of 2
Watch the leftovers: trades only happen in fixed bundles (3 blue, 2 red).
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Approach: trade in bundles and track leftovers
- 16 blue ÷ 3 gives 5 red marbles (1 blue left over).
- 5 red ÷ 2 gives 2 trades = 10 green marbles (1 red left over).
- The maximum number of green marbles is 10 (B).
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