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2012 Math Kangaroo

Problem 11

Problem 11 · 2012 Math Kangaroo Medium
Algebra & Patterns work-backwardsum-constraint

Grandmother gave Vivian and Mike some apples and pears. In total they had 25 pieces of fruit. On the way home Vivian ate 1 apple and 3 pears, and Mike ate 3 apples and 2 pears. At home they noticed that there were exactly the same number of apples and pears left in the basket. How many pears had Grandmother given them?

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Answer: B — 13
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Hint 1 of 2
Work out how many apples and pears were eaten in total.
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Hint 2 of 2
After eating, the basket has equal apples and pears; build back up to the pears given.
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Approach: track what was eaten, then use the equal-leftover clue
  1. Eaten: Vivian 1 apple + 3 pears, Mike 3 apples + 2 pears, so 4 apples and 5 pears eaten (9 pieces).
  2. Left in the basket: 25 - 9 = 16 pieces, split equally, so 8 apples and 8 pears.
  3. Total pears = pears left + pears eaten = 8 + 5 = 13.
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