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2021 Math Kangaroo

Problem 22

Problem 22 · 2021 Math Kangaroo Stretch
Arithmetic & Operations part-of-totalcareful-counting

Each of the 5 boxes contains either apples or bananas, but not both. The total weight of all the bananas is 3 times the weight of all the apples. Which boxes contain apples?

Figure for Math Kangaroo 2021 Problem 22
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Answer: E — 1 and 4
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Hint 1 of 2
If the bananas weigh 3 times the apples, then for every 1 kg of apples there are 3 kg of bananas — so apples are 1 part out of 4 equal parts of the whole.
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Hint 2 of 2
Add all five box weights, take a quarter of that for the apples, then find which boxes add up to it.
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Approach: apples are one quarter of the total weight
  1. The five boxes weigh 7, 5, 6, 2, 16, totalling 36 kg.
  2. Bananas are 3 times the apples, so apples make up 36 / 4 = 9 kg.
  3. Boxes summing to 9 kg are the 7 kg and 2 kg ones, i.e. boxes 1 and 4.
  4. So the apple boxes are 1 and 4 (E).
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