The total cost of 7 sweaters and 7 coats was $329. Tina bought 9 such sweaters, 7 such coats and a cardigan for $420. If the total cost of a jacket and a sweater was $59, find the difference in cost between the sweater and the jacket.
Let 1 S be 1 sweater.
Let 1 C be 1 coat.
Let 1 J be 1 jacket.

7 S + 7 C = 329 --- (1)

1 S + 1 C = 329 ÷ 7
1 S + 1 C = 47 --- (2)

1 S + 1 J = 59 --- (3)

9 S + 7 C + 1 J = 420 --- (4)

(4) - (1)
(9 S + 7 C + 1 J) - (7 S + 7 C) = 420 - 329 
9 S - 7 S + 7 C - 7 C + 1 J = 91

2 S + 1 J = 91 --- (5)

(5) - (3)
(2 S + 1 J) - (1 S + 1 J) = 91 - 59
2 S - 1 S + 1 J - 1 J = 32
2 S - 1 S = 32

1 S = 32

From (3)
1 S + 1 J = 59
32 + 1 J = 59

1 J = 59 - 32 = 27

Difference in the cost between the sweater and the jacket
= 1 S - 1 J
= 32 - 27
= $5

Answer(s): $5