Question

7) Skyler buys 8 T-shirts and 5 hats for $220. The next week, he buys 5 T-shirts and 1 had for $112. How

much does each T-shirt and each hat cost? Write a system of equations that can be used to solve the problem.

Answer 1

The cost of each T-shirt and each hat is $20 and $12 respectively.

Explanation:

As given in question that Skyler buys 8 T-shirts and 5 hats for $220.

The next day, he buys 5 T-shirts and 1 hat for $112.

We have to find the cost of T-shirt and hat each.

Let the cost of T-shirt and hat is x and y respectively.

According to the question,

8x + 5y = 220 ............(i)

5x + 1y = 112 ............(ii)

Multiply by 5 in eq. (ii)

25x + 5y = 560 ............(iii)

Now subtract eq. (iii) - eq. (i)

25x + 5y = 560

- 8x + 5y = 220

17x = 340

`x = (340)/(17)`

∴ x = 20

Put the value of x in eq. (ii)

5 x 20 + y = 112

100 + y = 112

y = 112 - 100

∴ y = 12

Hence the cost of each T-shirt and each hat is $20 and $12 respectively.