Zoe made a profit of 50% from the sale of a dress and a profit of 70% from the sale of a sweater. The total profit she made from the two items was $81. She later sold a similar dress at a discount of 25% off the advertised price. Her total profit for the three items then increased to $85.50.

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

	Dress 1	Sweater 1	Dress 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 dress
= 100% of the price of the dress + 50% of the price of the dress
= 2 u + 1 u
= 3 u

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

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

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

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

0.25 u = 85.5 - 81 = 4.5

1 u = 4.5 ÷ 0.25 = 18

1 u + 7 p = 81
1 x 18 + 7 p = 81
18 + 7 p = 81

7 p
= 81 - 18
= $63

Profit made on the sweater = $63

(b)
1 p = 63 ÷ 7 = 9

Selling price of the sweater
= 17 p
= 17 x 9
= $153

Answer(s): (a) $63; (b) $153