Problem 16 · 2025 Math Kangaroo
Medium
Algebra & Patterns
percent-multipliersubstitution
Paul shoots a ball at two targets (see diagram) a total of 27 times. When he aims for the upper-left target, he hits 50% of the time, and when he aims for the bottom-right target, he hits 80% of the time. In total, 9 of his shots miss their target. How many times does Paul hit the top-left target?
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Answer: C — 6
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Hint 1 of 2
27 shots, 9 missed, so 18 hit; let a shots aim upper-left and b aim lower-right.
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Hint 2 of 2
Misses are 50% of a plus 20% of b; set that equal to 9.
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Approach: set up the miss equation
- a + b = 27 shots. Misses: 0.5a + 0.2b = 9.
- Substitute b = 27−a: 0.5a + 0.2(27−a) = 9 → 0.3a = 3.6 → a = 12.
- Hits on the upper-left = 50% of 12 = 6.
Mark:
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