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

Answer:

• 1 sweater: $13
• 1 shirt: $8

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

__

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

_____

A graphing calculator can help you check your work.