Problem 17 · 2023 Math Kangaroo
Medium
Arithmetic & Operations
Algebra & Patterns
substitutioncasework
Tom, John and Lily have each shot 6 arrows at a disc with three sections (see diagram). The number of points for a hit depends on the section that has been hit. Tom has 46 points and John has 34 points. How many points did Lily get?
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Answer: D — 40
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Hint 1 of 2
Let the three ring values be the unknowns and read off how many arrows landed in each ring for Tom and John.
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Hint 2 of 2
Two equations fix enough about the ring values to total Lily's hits.
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Approach: set up the ring point-values from Tom and John, then total Lily
- Let the outer, middle and inner rings be worth fixed point values; each player threw 6 arrows.
- Tom's hits give 46 points and John's give 34 points, which pin down the ring values (each is consistent with 6 arrows).
- Applying those values to Lily's six hits totals 40.
- So the answer is 40 (D).
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