Problem 23 · 2019 Math Kangaroo
Stretch
Arithmetic & Operations
total-then-dividework-backward
Jette and Willi throw balls at two identically built pyramids, each made up of 15 tins (each tin is worth the number written on it). The pictures show each pyramid after Jette's throw and after Willi's throw. Jette hits 6 tins and gets 25 points. Willi hits 4 tins. How many points does Willi get?
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Answer: D — 26
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Hint 1 of 3
Both pyramids are built the same, so each one holds the same total number of points.
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Hint 2 of 3
Use Jette's picture: the tins left standing plus the 25 she knocked down give the whole pyramid's total.
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Hint 3 of 3
For Willi, that same total minus the tins still standing in his picture is his score.
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Approach: find the grand total, then subtract what's left
- After Jette's throw the standing tins add up to 55, and the 6 she knocked down scored 25, so the whole pyramid totals 55 + 25 = 80.
- After Willi's throw the standing tins add up to 54.
- So Willi's 4 knocked tins score 80 − 54 = 26 (D).
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