Olivia made a profit of 40% from the sale of a shirt and a profit of 60% from the sale of a sweater. The total profit she made from the two items was $68. 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 $70.50.
- Find the profit made on the sweater.
- How much did she sell the sweater for?
|
Shirt 1 |
Sweater 1 |
Shirt 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 |
|
|
- 1.75 u |
Discounted Price |
|
|
5.25 u |
100% + 40% = 140%
140% =
140100 =
75100% + 60% = 160%
160% =
160100 =
85(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 + 60% of the price of the sweater
= 5 p + 3 p
= 8 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 = 70.5 - 68 = 2.5
1 u = 2.5 ÷ 0.25 = 10
2 u + 3 p = 68
2 x 10 + 3 p = 68
20 + 3 p = 68
3 p
= 68 - 20
= $48
Profit made on the sweater = $48
(b)
1 p = 48 ÷ 3 = 16
Selling price of the sweater
= 8 p
= 8 x 16
= $128
Answer(s): (a) $48; (b) $128