The total cost of 3 jackets and 3 shirts was $126. Tina bought 5 such jackets, 3 such shirts and a cardigan for $206. If the total cost of a vest and a jacket was $52, find the difference in cost between the jacket and the vest.
Let 1 J be 1 jacket.
Let 1 S be 1 shirt.
Let 1 V be 1 vest.

3 J + 3 S = 126 --- (1)

1 J + 1 S = 126 ÷ 3
1 J + 1 S = 42 --- (2)

1 J + 1 V = 52 --- (3)

5 J + 3 S + 1 V = 206 --- (4)

(4) - (1)
(5 J + 3 S + 1 V) - (3 J + 3 S) = 206 - 126 
5 J - 3 J + 3 S - 3 S + 1 V = 80

2 J + 1 V = 80 --- (5)

(5) - (3)
(2 J + 1 V) - (1 J + 1 V) = 80 - 52
2 J - 1 J + 1 V - 1 V = 28
2 J - 1 J = 28

1 J = 28

From (3)
1 J + 1 V = 52
28 + 1 V = 52

1 V = 52 - 28 = 24

Difference in the cost between the jacket and the vest
= 1 J - 1 V
= 28 - 24
= $4

Answer(s): $4