Lucy made a profit of 50% from the sale of a blouse and a profit of 60% from the sale of a sweater. The total profit she made from the two items was $64. She later sold a similar blouse at a discount of 25% off the advertised price. Her total profit for the three items then increased to $67.25.

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

	Blouse 1	Sweater 1	Blouse 2
Cost Price	2 u	5 p	2 u
Profit	+ 1 u	+ 3 p	+ 1 u
Selling Price	3 u	8 p	3 u
Discount			- 0.75 u
Discounted Price			2.25 u

100% + 50% = 150%
150% = ¹⁵⁰₁₀₀ = ³₂

100% + 60% = 160%
160% = ¹⁶⁰₁₀₀ = ⁸₅

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

Selling price of the sweater
= 100% of the price of the sweater + 60% of the price of the sweater
= 5 p + 3 p
= 8 p

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

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

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

0.25 u = 67.25 - 64 = 3.25

1 u = 3.25 ÷ 0.25 = 13

1 u + 3 p = 64
1 x 13 + 3 p = 64
13 + 3 p = 64

3 p
= 64 - 13
= $51

Profit made on the sweater = $51

(b)
1 p = 51 ÷ 3 = 17

Selling price of the sweater
= 8 p
= 8 x 17
= $136

Answer(s): (a) $51; (b) $136