Min made a profit of 40% from the sale of a shirt and a profit of 70% from the sale of a sweater. The total profit she made from the two items was $71. She later sold a similar shirt at a discount of 25% off the advertised price. Her total profit for the three items then increased to $75.50.

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

	Shirt 1	Sweater 1	Shirt 2
Cost Price	5 u	10 p	5 u
Profit	+ 2 u	+ 7 p	+ 2 u
Selling Price	7 u	17 p	7 u
Discount			- 1.75 u
Discounted Price			5.25 u

100% + 40% = 140%
140% = ¹⁴⁰₁₀₀ = ⁷₅

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

(a)
Selling price of the shirt
= 100% of the price of the shirt + 40% of the price of the shirt
= 5 u + 2 u
= 7 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 shirt after 25% discount in percentage
= 100% - 25%
= 75%

Price of the second shirt after 25% discount in units
= 75% x 7 u
= ⁷⁵₁₀₀ x 7 u
= 5.25 u

Profit made for the second shirt in units
= 5.25 u - 5 u
= 0.25 u

0.25 u = 75.5 - 71 = 4.5

1 u = 4.5 ÷ 0.25 = 18

2 u + 7 p = 71
2 x 18 + 7 p = 71
36 + 7 p = 71

7 p
= 71 - 36
= $35

Profit made on the sweater = $35

(b)
1 p = 35 ÷ 7 = 5

Selling price of the sweater
= 17 p
= 17 x 5
= $85

Answer(s): (a) $35; (b) $85