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2017 Math Kangaroo

Problem 10

Problem 10 · 2017 Math Kangaroo Medium
Arithmetic & Operations careful-countingsum-constraint

Old McDonald has a horse, two cows and three pigs. How many more cows does he need, so that exactly half of all his animals are cows?

Figure for Math Kangaroo 2017 Problem 10
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Answer: C — 2
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Hint 1 of 2
Count the animals that are NOT cows; that group never changes.
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Hint 2 of 2
Half being cows means the cows must end up matching the not-cows in number.
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Approach: balance cows against the rest
  1. He has 1 horse, 2 cows and 3 pigs: 6 animals, of which 4 are not cows.
  2. For cows to be exactly half, the cows must equal the non-cows, which stay at 4.
  3. He has 2 cows, so he needs 4 - 2 = 2 more.
  4. He needs 2 more cows.
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