Problem 25 · 2011 Math Kangaroo
Stretch
Algebra & Patterns
substitutionpercent-multiplier
Myshko shoots at a target board. He only hits the numbers 5, 8 and 10. In doing so he hits the numbers 8 and 10 equally often and scores a total of 99 points. For 25% of his shots he missed the target board completely. How often did he shoot at the target board?
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Answer: D — 20
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Hint 1 of 2
Call the equal counts of the 8s and 10s the same letter and write the score equation.
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Hint 2 of 2
Once you know how many shots hit, use 'missed 25%' to scale up to all shots.
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Approach: set hits of 8 and 10 equal, use the score, then the 25% miss rate
- Let him hit 8 and 10 the same number of times, k each, and 5 some number m times.
- Score: 5m + 8k + 10k = 5m + 18k = 99; trying k = 3 gives m = 9.
- Hits = m + 2k = 15, and since 25% missed, hits are 75% of all shots, so total = 15/0.75 = 20.
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