Gwen made a profit of 40% from the sale of a jacket and a profit of 80% from the sale of a vest. The total profit she made from the two items was $54. She later sold a similar jacket at a discount of 20% off the advertised price. Her total profit for the three items then increased to $64.20.

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

	Jacket 1	Vest 1	Jacket 2
Cost Price	5 u	5 p	5 u
Profit	+ 2 u	+ 4 p	+ 2 u
Selling Price	7 u	9 p	7 u
Discount			- 1.4 u
Discounted Price			5.6 u

100% + 40% = 140%
140% = ¹⁴⁰₁₀₀ = ⁷₅

100% + 80% = 180%
180% = ¹⁸⁰₁₀₀ = ⁹₅

(a)
Selling price of the jacket
= 100% of the price of the jacket + 40% of the price of the jacket
= 5 u + 2 u
= 7 u

Selling price of the vest
= 100% of the price of the vest + 80% of the price of the vest
= 5 p + 4 p
= 9 p

Price of the second jacket after 20% discount in percentage
= 100% - 20%
= 80%

Price of the second jacket after 20% discount in units
= 80% x 7 u
= ⁸⁰₁₀₀ x 7 u
= 5.6 u

Profit made for the second jacket in units
= 5.6 u - 5 u
= 0.6 u

0.6 u = 64.2 - 54 = 10.2

1 u = 10.2 ÷ 0.6 = 17

2 u + 4 p = 54
2 x 17 + 4 p = 54
34 + 4 p = 54

4 p
= 54 - 34
= $20

Profit made on the vest = $20

(b)
1 p = 20 ÷ 4 = 5

Selling price of the vest
= 9 p
= 9 x 5
= $45

Answer(s): (a) $20; (b) $45