Lynn made a profit of 50% from the sale of a skirt and a profit of 70% from the sale of a vest. The total profit she made from the two items was $53. She later sold a similar skirt at a discount of 20% off the advertised price. Her total profit for the three items then increased to $57.40.

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

	Skirt 1	Vest 1	Skirt 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			- 0.6 u
Discounted Price			2.4 u

100% + 50% = 150%
150% = ¹⁵⁰₁₀₀ = ³₂

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

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

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

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

Price of the second skirt after 20% discount in units
= 80% x 3 u
= ⁸⁰₁₀₀ x 3 u
= 2.4 u

Profit made for the second skirt in units
= 2.4 u - 2 u
= 0.4 u

0.4 u = 57.4 - 53 = 4.4

1 u = 4.4 ÷ 0.4 = 11

1 u + 7 p = 53
1 x 11 + 7 p = 53
11 + 7 p = 53

7 p
= 53 - 11
= $42

Profit made on the vest = $42

(b)
1 p = 42 ÷ 7 = 6

Selling price of the vest
= 17 p
= 17 x 6
= $102

Answer(s): (a) $42; (b) $102