The total cost of 9 sweaters and 9 vests was $513. Tina bought 11 such sweaters, 9 such vests and a cardigan for $623. If the total cost of a jumpsuit and a sweater was $71, find the difference in cost between the sweater and the jumpsuit.
Let 1 S be 1 sweater.
Let 1 V be 1 vest.
Let 1 J be 1 jumpsuit.

9 S + 9 V = 513 --- (1)

1 S + 1 V = 513 ÷ 9
1 S + 1 V = 57 --- (2)

1 S + 1 J = 71 --- (3)

11 S + 9 V + 1 J = 623 --- (4)

(4) - (1)
(11 S + 9 V + 1 J) - (9 S + 9 V) = 623 - 513 
11 S - 9 S + 9 V - 9 V + 1 J = 110

2 S + 1 J = 110 --- (5)

(5) - (3)
(2 S + 1 J) - (1 S + 1 J) = 110 - 71
2 S - 1 S + 1 J - 1 J = 39
2 S - 1 S = 39

1 S = 39

From (3)
1 S + 1 J = 71
39 + 1 J = 71

1 J = 71 - 39 = 32

Difference in the cost between the sweater and the jumpsuit
= 1 S - 1 J
= 39 - 32
= $7

Answer(s): $7