Acoach 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? a. 6 b. 11 c. 18 d. 23

First, we define variables:
 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
 
 the coach did purchase 23 large hats
 d. 23

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