Olivia made a profit of 50% from the sale of a coat and a profit of 80% from the sale of a dress. The total profit she made from the two items was $32. She later sold a similar coat at a discount of 20% off the advertised price. Her total profit for the three items then increased to $35.20.

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

	Coat 1	Dress 1	Coat 2
Cost Price	2 u	5 p	2 u
Profit	+ 1 u	+ 4 p	+ 1 u
Selling Price	3 u	9 p	3 u
Discount			- 0.6 u
Discounted Price			2.4 u

100% + 50% = 150%
150% = ¹⁵⁰₁₀₀ = ³₂

100% + 80% = 180%
180% = ¹⁸⁰₁₀₀ = ⁹₅

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

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

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

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

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

0.4 u = 35.2 - 32 = 3.2

1 u = 3.2 ÷ 0.4 = 8

1 u + 4 p = 32
1 x 8 + 4 p = 32
8 + 4 p = 32

4 p
= 32 - 8
= $24

Profit made on the dress = $24

(b)
1 p = 24 ÷ 4 = 6

Selling price of the dress
= 9 p
= 9 x 6
= $54

Answer(s): (a) $24; (b) $54