Roshel made a profit of 50% from the sale of a sweater and a profit of 80% from the sale of a jacket. The total profit she made from the two items was $89. She later sold a similar sweater at a discount of 10% off the advertised price. Her total profit for the three items then increased to $98.10.

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

	Sweater 1	Jacket 1	Sweater 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			- 0.3 u
Discounted Price			2.7 u

100% + 50% = 150%
150% = ¹⁵⁰₁₀₀ = ³₂

100% + 80% = 180%
180% = ¹⁸⁰₁₀₀ = ⁹₅

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

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

Price of the second sweater after 10% discount in percentage
= 100% - 10%
= 90%

Price of the second sweater after 10% discount in units
= 90% x 3 u
= ⁹⁰₁₀₀ x 3 u
= 2.7 u

Profit made for the second sweater in units
= 2.7 u - 2 u
= 0.7 u

0.7 u = 98.1 - 89 = 9.1

1 u = 9.1 ÷ 0.7 = 13

1 u + 4 p = 89
1 x 13 + 4 p = 89
13 + 4 p = 89

4 p
= 89 - 13
= $76

Profit made on the jacket = $76

(b)
1 p = 76 ÷ 4 = 19

Selling price of the jacket
= 9 p
= 9 x 19
= $171

Answer(s): (a) $76; (b) $171