Problem 7 · 2020 Math Kangaroo
Medium
Algebra & Patterns
substitutionsum-constraint
In a garden, a bush has branches with seven leaves, or branches with four leaves and a flower. Janaina counted the leaves and flowers and found that the bush has 9 flowers and 120 leaves. How many branches does the bush have?
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Answer: B — 21
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Hint 1 of 2
Each flower comes with a four-leaf branch, so the 9 flowers account for 9 such branches.
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Hint 2 of 2
Subtract those branches' leaves from 120, then divide the rest among seven-leaf branches.
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Approach: split the count into flowered and unflowered branches
- A branch with a flower has 4 leaves; 9 flowers mean 9 of these branches, giving 9x4 = 36 leaves.
- That leaves 120 - 36 = 84 leaves on the seven-leaf branches, i.e. 84 / 7 = 12 branches.
- Total branches = 9 + 12 = 21.
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