Question

A manager purchased a total of 38 souvenir shirts and hats. Each shirt cost $4.50 and each hat cost $3.25. The numberof shirts the manager ordered was two morethan twice the number of hats.

Answer 1

We can create the following system of equations:

(1) Number of shirts the manager ordered was two more than twice the number of hats:

Let x be the number of shirts

Let y be the number of hats

`x=2y+2`

(2) manager purchased a total of 38 souvenir:

`x+y=38`

Since we have our system of equations, to solve it we can isolate one variable from equation (2) and substitute it in equation (1):

`y=38-x`

(2) in (1):

`\begin{gathered} x=2(38-x)+2 \\ x=76-2x+2 \\ 2x+x=76+2 \\ 3x=78 \\ x=(78)/(3) \\ x=26 \end{gathered}`

He purchased 26 shirts.

Now, with the x-value we are going to substitute it in (2) to find the y-value(number of hats purchased)

`\begin{gathered} y=38-26 \\ y=12 \end{gathered}`

He purchased 12 hats.

Answer:

He purchased 26 shirts and 12 hats.