The total cost of 4 vests and 4 blazers was $232. Tina bought 6 such vests, 4 such blazers and a cardigan for $322. If the total cost of a coat and a vest was $56, find the difference in cost between the vest and the coat.
Let 1 V be 1 vest.
Let 1 B be 1 blazer.
Let 1 C be 1 coat.

4 V + 4 B = 232 --- (1)

1 V + 1 B = 232 ÷ 4
1 V + 1 B = 58 --- (2)

1 V + 1 C = 56 --- (3)

6 V + 4 B + 1 C = 322 --- (4)

(4) - (1)
(6 V + 4 B + 1 C) - (4 V + 4 B) = 322 - 232 
6 V - 4 V + 4 B - 4 B + 1 C = 90

2 V + 1 C = 90 --- (5)

(5) - (3)
(2 V + 1 C) - (1 V + 1 C) = 90 - 56
2 V - 1 V + 1 C - 1 C = 34
2 V - 1 V = 34

1 V = 34

From (3)
1 V + 1 C = 56
34 + 1 C = 56

1 C = 56 - 34 = 22

Difference in the cost between the vest and the coat
= 1 V - 1 C
= 34 - 22
= $12

Answer(s): $12