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.

Step-by-step explanation:

We can let x and y represent the costs of a sweater and shirt, respectively. Then the two purchases can be described by ...

  x + 4y = 45

  4x + 5y = 92

Subtracting the second equation from 4 times the first eliminates the x-variable:

  4(x +4y) -(4x +5y) = 4(45) -(92)

  11y = 88 . . . . simplify

  y = 8 . . . . . . .divide by 11

Substituting into the first equation gives ...

  x + 4·8 = 45

  x = 13 . . . . . . subtract 32

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The price of one sweater is $13; one shirt is $8.

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A graphing calculator can help you check your work.

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