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