Sarah buys a skirt, a sweater, a vest and a jacket. The average cost of these items is $30. The total cost of the vest and the jacket is ³₅ of the total cost of the skirt and the sweater. If the skirt costs $17.90 and the jacket costs $7.10, find the difference in cost between the sweater and the vest.
Total cost of the 4 items
= 4 x 30
= $120

Total cost of the vest and the jacket = 3 u
Total cost of the skirt and the sweater = 5 u

Total cost of the 4 items
= 3 u + 5 u
= 8 u

8 u = 120

1 u = 120 ÷ 8 = 15

Total cost of the vest and the jacket
= 3 u
= 3 x 15
= $45

Cost of the vest
= 45 - 7.10
= $37.90

Total cost of the skirt and the sweater
= 5 u
= 5 x 15
= $75

Cost of the sweater
= 75 - 17.90
= $57.10

Difference in cost between the sweater and the vest
= 57.10 - 37.90
= $19.20

Answer(s): $19.20