Question

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?

Answer 1

Answer:

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

Answer 2

Let T-shirt be "x"

Let Hat be "y"

$8x + 5y = 220 \\ 5x + (1)y = 112$

Now in order to solve the two equations you need to multiply the second equation by -5. You will get:


$- 25x - 5y = - 560$

Now add the two equations:


$(8x - 25x) + (5y - 5y) = 220 - 560 \\ - 17x = - 340 \\ x = 20$

Now substitute the value of x in first equation in order to get the value of y.


$8(20) + 5y = 220 \\ 160 + 5y = 220 \\ 5y = 220 - 160 \\ 5y = 60 \\ y = 12$

So the value of one T-Shirt is $20

and the value of one Hat is $12