A coach purchases 47 hats for his players and their families at a total cost of $302. The cost of a small hat is $5.50. A medium hat costs $6.00. A large hat costs $7.00. He purchases three times as many medium hats as small hats. Using matrices, how many large hats did the coach purchase? 6
11
18
23

d. 23

Step-by-step explanation:

 x: small hat

 y: medium hat

 z: large hat

 We now write the system of equations:

 x + y + z = 47

 5.50x + 6y + 7z = 302

 -3x + y = 0

 We can write the system in matrix form as:

 Ax = b

 Where,

 A = [1  1  1; 5.50  6  7; -3  1  0]

 b = [47;  302;  0]

 x = [x;  y ;  z]

 Solving the system we have:

 x = 6

 y = 18

 z = 23

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the answer is c

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