Skyler buys 8 t-shirts and 5 hats for $220. the next day, he buys 5 t-shirts and 1 hat for $112. what is the cost of each t-shirt and each hat?

shirt =20

hat =12

Step-by-step explanation:

cost of shirts * number of shirts + cost of hats * number of hats = total cost

Let the cost of shirts = s and the cost of hats =h

s * 8 +  h * 5 = 220

s * 5 + h * 1 = 112

We will use elimination to solve this system of equations.  Multiply the second equation by -5.

-5(s * 5 + h * 1) =-5( 112)

-25s -5h = -560

Now we need to add it to the first equation

 8s + 5h = 220

-25s - 5h = -560

-17s          = -340

Divide each side by -17

-17s/-17 = -340/-17

s = 20

The cost of a shirt is $20

Now we need to find the cost of a hat.

5s+h = 112

Substitute s=20 into the above equation.

5(20)+h = 112

100+h = 112

Subtract 100 from each side.

100-100+h = 112-100

h= 12

The cost of a hat is 12