Question

If 7 shirts and 4 sweaters cost $192, and 8 shirts and 7 sweaters cost $268, what is the cost of one shirt and what is the

Answer 1

Answer:

The cost of one shirt is $16 and the cost of one sweater is $20.

Step-by-step explanation:

Let the cost of one shirt be x and the cost of one shirt be y.

7x + 4y = 192 -----Equation 1

8x + 7y = 268 -----Equation 2

Equations 2-1:

8x + 7y - 7x - 4y = 268 - 192

x + 3y = 76

x = 76-3y -----Equation 3

Subsitute x = 76-3y into Equation 1:

7x + 4y = 192

7(76-3y) + 4y = 192

532 - 21y + 4y = 192

532 - 17y = 192

-17y = 192-532

-17y = -340

17y = 340

y = 340 ÷ 17

y = 20 (The cost of one sweater is $20)

Substitute y = 20 into Equation 3:

x = 76-3y

x = 76 -3(20)

x = 76 - 60

x = 16 (The cost of one shirt is $16)