Answer:
- $2.49 each shirt
- $3.99 each slacks
- $7.49 each sports coat
Step-by-step explanation:
If we let s, p, c represent the cost of cleaning the shirts, pants, and coats, respectively, the problem information lets us write three equations:
3s +1p +0c = 11.46
5s +2p +1c = 27.92
5s +0p +1c = 19.94
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A variety of methods and tools are available for solving these equations. We can do it "by hand" using elimination and substitution.
Subtracting the 3rd equation from the 2nd, we get ...
(5s +2p +c) -(5s +c) = (27.92) -(19.94)
2p = 7.98
p = 7.98/2 = 3.99
Substituting this value into the first equation gives ...
3s +1(3.99) = 11.46
3s = 7.47 . . . . . . . . . . subtract 3.99
s = 7.47/3 = 2.49
Substituting this value into the last equation gives ...
5(2.49) +c = 19.94
c = 7.49 . . . . . . . . . . . subtract 12.45
Rachel was charged ...
$2.49 for each shirt
$3.99 for each pair of slacks
$7.49 for each sports coat
