The total cost of 6 shirts and 6 coats was $246. Tina bought 8 such shirts, 6 such coats and a cardigan for $336. If the total cost of a vest and a shirt was $59, find the difference in cost between the shirt and the vest.
Let 1 S be 1 shirt.
Let 1 C be 1 coat.
Let 1 V be 1 vest.

6 S + 6 C = 246 --- (1)

1 S + 1 C = 246 ÷ 6
1 S + 1 C = 41 --- (2)

1 S + 1 V = 59 --- (3)

8 S + 6 C + 1 V = 336 --- (4)

(4) - (1)
(8 S + 6 C + 1 V) - (6 S + 6 C) = 336 - 246 
8 S - 6 S + 6 C - 6 C + 1 V = 90

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

(5) - (3)
(2 S + 1 V) - (1 S + 1 V) = 90 - 59
2 S - 1 S + 1 V - 1 V = 31
2 S - 1 S = 31

1 S = 31

From (3)
1 S + 1 V = 59
31 + 1 V = 59

1 V = 59 - 31 = 28

Difference in the cost between the shirt and the vest
= 1 S - 1 V
= 31 - 28
= $3

Answer(s): $3