A coach purchases 47 hats for his players and their families at a total cost of 302 dollars The cost of a small hat is 5 point 5 0 dollars A medium hat costs 6 point 0 0 dollars A large hat costs 7 point 0 0 dollars He purchases three times as many medium hats as small hats. Using matrices, how many large hats did the coach purchase?

Let s, m, and l represent the numbers of small, medium, and large hats. The information gives s + m + l = 47 and 5.50s + 6m + 7l = 302, with m = 3s. Substituting m = 3s gives 4s + l = 47 and 23.50s + 7l = 302; solving these equations gives s = 6 and l = 23. The coach purchased 23 large hats, choice A.

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