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Problem 777

AMC 12 late, AIME early

Algebra Difficulty 4.2 Find the answer Berkeley Math Circle: Monthly Contest 2 · United States

You are out walking and see a group of rhinoceroses (which each have two horns and four legs) and triceratopses (which each have three horns and four legs). If you count 31 horns and 48 legs, how many triceratopses are there?

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Official solution

Solution:

Since each animal has 4 legs, there must be $48 / 4 = 12$ animals. Each triceratops has 3 horns and each rhinoceros has 2, so if there are $t$ triceratopses and $r$ rhinoceroses we get $t + r = 12$ and $3t + 2r = 31$ . Subtracting twice the first equation from the second gives $t = 7$ .

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