Question

Michael paid $120 for 4 shirts and 4 ties. 3 shirts cost as much as 2 ties. How much did a shirt cost?

Answer 1

s = price of shirt

t = price of tie

Michael paid $120 for 4 shirts and 4 ties means:

4 s + 4 t = 120

Divide both sides by 4

s + t = 30

3 shirts cost as much as 2 ties means:

3 s = 2 t

Divide both sides by 2

3 / 2 s = t

t = 3 / 2 s

Replace this value in equation:

s + t = 30

s + 3 / 2 s = 30

2 / 2 s + 3 / 2 s = 30

5 / 2 s = 30

Multiply both sides by 2

5 s = 60

s = 60 / 5

s = $12

Check result:

t = 3 / 2 s

t = 3 / 2 ∙ 12

t = 36 / 2 = 18

t = $18

4 s + 4 t = 4 ∙ $ 12 + 4 ∙ $ 18 = $48 + $72 = $120

3 s = 2 t

3 ∙ $ 12 = 2 ∙ $ 18

$36 = $36