Question

Mike took clothes to the cleaners three times last month.​ First, he brought 4 shirts and 1 pair of slacks and paid ​$15.95. Then he brought 7 ​shirts, 4 pairs of​ slacks, and 1 sports coat and paid ​$49.38. ​Finally, he brought 3 shirts and 1 sports coat and paid ​$15.46. How much was he charged for each​ shirt, each pair of​ slacks, and each sports​ coat? Mike was charged ​$ nothing for each​ shirt, ​$ nothing for each pair of​ slacks, and ​$ nothing for each sports coat.

Answer 1

Each Shirt ≈ $2.49

Each Pair of Slacks ≈ $5.99

Each Sports Coat ≈ $7.99

Explanation:

Mike took clothes to the cleaners three times last month.​

Let S denotes shirts, P denotes pair of slacks and C denotes sports coat.

First, he brought 4 shirts and 1 pair of slacks and paid ​$15.95.

Mathematically,

4S + P = 15.95 eq. 1

Then he brought 7 ​shirts, 4 pairs of​ slacks, and 1 sports coat and paid ​$49.38.

Mathematically,

7S + 4P + C = 49.38 eq. 2

​Finally, he brought 3 shirts and 1 sports coat and paid ​$15.46.

Mathematically,

3S + C = 15.46 eq. 3

We are asked to find how much was he was charged for each​ shirt, each pair of​ slacks, and each sports​ coat.

4S + P + 0C = 15.95 eq. 1

7S + 4P + C = 49.38 eq. 2

3S + 0P + C = 15.46 eq. 3

We have 3 equations and 3 unknowns, they can be solved simultaneously using calculator or using online system of equations solver.

Using online system of equations solver yields,

S ≈ $2.49

P ≈ $5.99

C ≈ $7.99

So that means Mike was charge $2.49 for each shirt, $5.99 for each pair of slacks and $7.99 for each sports coat.