Gwen made a profit of 50% from the sale of a vest and a profit of 70% from the sale of a coat. The total profit she made from the two items was $105. She later sold a similar vest at a discount of 25% off the advertised price. Her total profit for the three items then increased to $108.50.

1. Find the profit made on the coat.
2. How much did she sell the coat for?

	Vest 1	Coat 1	Vest 2
Cost Price	2 u	10 p	2 u
Profit	+ 1 u	+ 7 p	+ 1 u
Selling Price	3 u	17 p	3 u
Discount			- 0.75 u
Discounted Price			2.25 u

100% + 50% = 150%
150% = ¹⁵⁰₁₀₀ = ³₂

100% + 70% = 170%
170% = ¹⁷⁰₁₀₀ = ¹⁷₁₀

(a)
Selling price of the vest
= 100% of the price of the vest + 50% of the price of the vest
= 2 u + 1 u
= 3 u

Selling price of the coat
= 100% of the price of the coat + 70% of the price of the coat
= 10 p + 7 p
= 17 p

Price of the second vest after 25% discount in percentage
= 100% - 25%
= 75%

Price of the second vest after 25% discount in units
= 75% x 3 u
= ⁷⁵₁₀₀ x 3 u
= 2.25 u

Profit made for the second vest in units
= 2.25 u - 2 u
= 0.25 u

0.25 u = 108.5 - 105 = 3.5

1 u = 3.5 ÷ 0.25 = 14

1 u + 7 p = 105
1 x 14 + 7 p = 105
14 + 7 p = 105

7 p
= 105 - 14
= $91

Profit made on the coat = $91

(b)
1 p = 91 ÷ 7 = 13

Selling price of the coat
= 17 p
= 17 x 13
= $221

Answer(s): (a) $91; (b) $221