Mai bought 3 pairs of socks and 2 pairs of shoes. A pair of shoes costs one dollar less than 5 times the price of a pair of socks. She spent $56.50. How much does a pair of socks cost and how much does a pair of shoes cost? (use one varible)

Cost of a pair of socks = x = $4.5

Cost of a pair of shoes = y = $21.5

Step-by-step explanation:

Let us represent

Cost of a pair of socks = x

Cost of a pair of shoes = y

Mai bought 3 pairs of socks and 2 pairs of shoes.

She spent $56.50.

Hence:

3x + 2y = 56.50

A pair of shoes costs one dollar less than 5 times the price of a pair of socks.

y = 5x - 1

Hence, we substitute 5x - 1 for y

3x + 2y = 56.50

3x + 2(5x - 1) = 56.5

3x + 10x - 2 = 56.5

13x - 2 = 56.5

13x = 56.5 + 2

13x = 58.5

x = 58.5/13

x = $4.50

Solving for y

y = 5x - 1

y = 5(4.5) - 1

y = 22.5 − 1

y = $ 21.5

Cost of a pair of socks = x = $4.5

Cost of a pair of shoes = y = $21.5