Mario took clothes to the cleaners three times last month. first, he brought 3 shorts and 1pair of slacks and $10.96. then, he brought 7 shirts, 2 pairs of slacks, and a sports coat and paid $30.40. finally, he brought 4 shirts and 1 sports coat and paid$14.45. how much was he charged for each shirt, each pair of slacks, and each sports coat.

Let us say that:

x = cost of shorts

y = cost of slacks

z = cost of sports coat

From the given statements, we can create the following equations:

eqtn 1: 3 x + y = 10.96

eqtn 2:  7 x + 2 y + z = 30.40

eqtn 3:  4 x + z = 14.45

Rewrite eqtn 1 explicit to y:

y = 10.96 – 3 x                    --> eqtn 4

Rewrite eqtn 3 explicit to z:

z = 14.45 – 4x                     --> eqtn 5

Plug in the values of y (eqtn 4) and z (eqtn 5) to eqtn 2:

7 x + 2 (10.96 – 3 x) + 14.45 – 4 x = 30.40

7 x + 21.92 – 6 x + 14.45 – 4 x = 30.40

- 3 x + 36.37 = 30.40

- 3 x = - 5.97

x = 1.99

Eqtn 4:

y = 10.96 – 3 x   

y = 10.96 – 3 (1.99)

y = 4.99

Eqtn 5:

z = 14.45 – 4x

z = 14.45 – 4 (1.99)

z = 6.49

Therefore each shirt cost $1.99, each slacks cost $4.99, and each sports coat cost $6.49.