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Algebra Difficulty 4.3 AIME Find the answer Slovenia

Peter breeds horses and cows on his farm. One day, the number of horses was the same as the number of cows and greater than $0$ . Then Peter bought some more cows so that the number of cows increased by $50\%$ . Now only $30\%$ of the animals are horses. How many horses does Peter have on his farm?

Pick one

Solution

Say at the beginning there were $x$ cows and $x$ horses on the farm. When the number of cows increased by $50\%$ , there were $x + \frac{1}{2}x = \frac{3}{2}x$ cows. Hence the ratio of horses was equal to $x/(x + \frac{3}{2}x) = \frac{2}{5}$ , which is $40\%$ and not $30\%$ . The correct answer is thus (E).

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