Sarah made a profit of 40% from the sale of a jacket and a profit of 60% from the sale of a vest. The total profit she made from the two items was $56. She later sold a similar jacket at a discount of 10% off the advertised price. Her total profit for the three items then increased to $76.80.

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

	Jacket 1	Vest 1	Jacket 2
Cost Price	5 u	5 p	5 u
Profit	+ 2 u	+ 3 p	+ 2 u
Selling Price	7 u	8 p	7 u
Discount			- 0.7 u
Discounted Price			6.3 u

100% + 40% = 140%
140% = ¹⁴⁰₁₀₀ = ⁷₅

100% + 60% = 160%
160% = ¹⁶⁰₁₀₀ = ⁸₅

(a)
Selling price of the jacket
= 100% of the price of the jacket + 40% of the price of the jacket
= 5 u + 2 u
= 7 u

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

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

Price of the second jacket after 10% discount in units
= 90% x 7 u
= ⁹⁰₁₀₀ x 7 u
= 6.3 u

Profit made for the second jacket in units
= 6.3 u - 5 u
= 1.3 u

1.3 u = 76.8 - 56 = 20.8

1 u = 20.8 ÷ 1.3 = 16

2 u + 3 p = 56
2 x 16 + 3 p = 56
32 + 3 p = 56

3 p
= 56 - 32
= $24

Profit made on the vest = $24

(b)
1 p = 24 ÷ 3 = 8

Selling price of the vest
= 8 p
= 8 x 8
= $64

Answer(s): (a) $24; (b) $64