Problem 19 · 2016 Math Kangaroo
Stretch
Arithmetic & Operations
sum-constraint
In a magic garden there are magic trees. On each tree there are either 6 pears and 3 apples, or 8 pears and 4 apples. In total there are 25 apples on the magic trees. How many pears in total are hanging on the magic trees altogether?
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Answer: D — 50
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Hint 1 of 2
Use the apple counts (3 per first kind of tree, 4 per second) to total 25 apples.
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Hint 2 of 2
Notice each apple comes with a fixed bundle of pears, so the pear total may not depend on the exact mix.
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Approach: find the tree counts from apples, then total the pears
- A '6-pears/3-apples' tree carries 2 pears per apple, and an '8-pears/4-apples' tree also carries 2 pears per apple.
- Since every apple is matched by exactly 2 pears on either kind of tree, the 25 apples come with 2 × 25 = 50 pears.
- So there are 50 pears in total.
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