Problem 12 · 2020 Math Kangaroo
Stretch
Algebra & Patterns
sum-constraint
Numbers were written on the petals of two flowers, one number on each petal. One of the petals is hidden. The sum of the numbers on the back flower is twice the sum of the numbers on the front flower. What number is written on the hidden petal?
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Answer: D — 30
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Hint 1 of 2
Add up the petals you can see on each flower separately.
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Hint 2 of 2
The back flower's total is double the front flower's total; the hidden petal makes up the difference.
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Approach: use the doubling relationship between the two totals
- The front flower shows all its numbers: 1 + 3 + 5 + 7 + 9 = 25.
- The back flower must total twice that, so 2 × 25 = 50.
- Its visible petals add to 2 + 4 + 6 + 8 = 20, so the hidden petal is 50 − 20 = 30.
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