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.

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.