Question

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

Answer 1

Choice D

Explanation:

Answer 2

d. 23

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

hope this helps

correct me if this is wrong