Problem 18 · 2025 Math Kangaroo
Hard
Logic & Word Problems
sum-constraintcasework
A witch has 10 apples, 9 bananas and 6 pears. One day she enchants all of her fruits into different types of fruit. For example, she turns each apple into either a banana or a pear. After that she has 15 apples, 7 bananas and 3 pears. How many apples did she turn into bananas?
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Answer: E — 7
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Hint 1 of 2
Every original fruit changes type, so all 10 apples leave and new apples arrive from other fruits.
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Hint 2 of 2
Set up the in/out counts for each fruit type and solve.
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Approach: track each fruit type in and out
- All 9 bananas and all 6 pears must become apples or each other; the 15 final apples come only from old bananas and pears.
- Since 9 + 6 = 15, every banana and every pear turned into an apple.
- Then the 10 apples must supply all 7 final bananas and 3 final pears: 7 + 3 = 10.
- So 7 apples became bananas.
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