Question

In a discount clothing​ store, all sweaters are sold at one fixed price and all shirts are sold at another fixed price. If one sweater and four shirts cost ​$45​, while four sweaters and five shirts cost ​$92​, find the price of one sweater and the price of one shirt.

Answer 1

Say SH is the shirt cost and SW is the sweater cost:
SW + 3SH = 42
3SW+2SH = 56

Solve the first for SW:
SW = 42-3SH

Plug that into the second:
3(42-3SH) +2SH = 56

Simplify:
126 - 9SH +2SH = 56
70 = 7SH
SH = 10

Plug this back into the SW formula:
SW = 42 - 3SH = 42 - 3*10 = 12

Shirts cost $10, sweaters cost $12.