Problem 9 · 2015 Math Kangaroo
Medium
Algebra & Patterns
sum-constraintsubstitution
Each plant in John's garden has exactly 5 leaves or exactly 2 leaves and a flower. In total the plants have 6 flowers and 32 leaves. How many plants are growing in the garden?
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Answer: A — 10
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Hint 1 of 2
Only the 2-leaf plants carry flowers, so the number of flowers tells you how many of those there are.
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Hint 2 of 2
Subtract the leaves on the flowering plants from 32 to see how many leaves are left for the 5-leaf plants.
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Approach: use the flowers to fix one kind of plant, then account for the leaves
- Each flower belongs to a 2-leaf plant, and there are 6 flowers, so there are 6 plants with 2 leaves, giving 6 × 2 = 12 leaves.
- That leaves 32 − 12 = 20 leaves for the 5-leaf plants, which is 20 ÷ 5 = 4 plants.
- Altogether 6 + 4 = 10 plants.
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