Commission and Retainer:

Salespeople are paid a commission (a percentage of sales) or a retainer (a fixed weekly income). The more sales that a salesperson makes, the greater is their income.

Useful rules are:

• Commission = Percent Commission × Sales
• Total Income = Commission + Retainer
• Sales = Commission × 100 ÷ Percent Commission

Example One - Commission

Salesman Sam earns 5% of whatever he sells. If he sells goods worth \$4000, what commission does he receive?

Commission
= Percent Commission × Sales
= 5% of \$4000
= 5100 × \$4000
= \$200

Example Two - Commission and Retainer

Salesman Sue earns a retainer of \$700 per week in addition to a commission of 3%. How much does she earn for selling goods worth \$20000.

Commission
= Percent Commission × Sales
= 3% × \$20000
= \$606

Total Income
= Commission + Retainer
= \$600 + \$700
= \$1300

Example Three - Finding the Original Sales

A salesperson works on a commission of 5% only. If she earns \$400 commission, what were the original sales?

Sales
= Commission × 100 ÷ Percent Commission
= \$400 × 100 ÷ 5
= \$8000

Questions - Commission and Retainer

Q1. Sophia earns a commission of 3.5% of all sales in addition to a weekly retainer of \$500. How much does she earn if her sales for one week are \$4000?
Q2. Zachary works on commission only. He earns 5% of all sales. If he earns \$800, how much were his sales?

A1. \$640
A2. \$16000

Discount:

A discount is an amount of money subtracted from the original price.
The discounted price is cheaper than the original price.

Useful rules are:

• Discount = Percent Discount × Original Price
• Discounted Price = Original Price – Discount
• Percent Discount = Discount ÷ Original Price × 100
• Original Price = Discounted Price × 100 ÷ Percent Discount

Example Four - Discounted Price

A hardware store offers a discount of 15% to builders. What is the discounted price for an electric drill whose original price is \$200?

Discount
= Percent Discount × Original price
= 15% × \$200
= \$30

Discounted Price
= Original Price – Discount
= \$200 – \$30
= \$170

The original price is 100%.
If the discount is 15%, then the discounted price = 100% – 15% = 85%.
Discounted price
= 85% of \$200
= \$170

Example Five - Finding Percent Discount

Coco received a discount of \$20 on a pair of shoes originally marked \$50. What percent discount is this?

Percent Discount
= Discount ÷ Original Price × 100
= \$20 ÷ \$50 × 100
= 40%

Example Six - Finding Original Price

A discount of 30% is equal to \$60. What was the original price?

Original Price
= Discount × 100 ÷ Percent Discount
= \$60 × 100 ÷ 30
= \$200

Questions - Discount

Q1. As a regular customer at a hardware store, Bob receives a discount of 30%. How much does he pay for timber originally priced at \$400?
Q2. Alana receives a discount of 10% and pays only \$900 for a kayak. What was the original price?
Q3. If a discount of \$50 is given for a set of water skis originally priced at \$500, what percent discount is this?

A1. \$280
A2. Discounted price = 90%; Original price = \$1000
A3. 10%

Profit:

A profit is an amount of money added to the original price.
The price with the added profit is more expensive than the original price.

Useful rules are:

• Profit = Percent Profit × Original Price
• Price with Profit = Original Price + Profit
• Percent Profit = Profit ÷ Original Price × 100

Example Seven - Price with Profit

A t-shirt store makes a profit of 35%. What is the price with profit for a t-shirt whose original price is \$20?

Profit
= Percent Profit × Original price
= 35% × \$20
= \$7

Price with profit
= Original Price + Profit
= \$20 + \$7
= \$27

The original price is 100%.
If the profit is 35%, then the price with profit = 100% + 35% = 135%.
Price with profit
= 135% of \$20
= \$27

Example Eight - Finding Percent Profit

If a car keyless entry remote ("beeper") is lost, the replacement cost is \$80. However, the cost of the software by the supplier is \$10. What is the profit? What is the percent profit?

Profit
= \$80 – \$10
= \$70

Percent Profit
= Profit ÷ Original Price × 100
= \$70 ÷ \$10 × 100
= 700%

Example Nine - Finding Original Price

A profit of 30% is equal to \$26. What was the original price?

Price with Profit
= 100% + 30%
= 130%

Original Price
= \$26 × 100 ÷ 130
= \$20

Questions - Profit

Q1. A store makes a profit of 40%. What is the price after profit of a skateboard originally priced at \$60?
Q2. The original price of a football was \$30. The added profit is \$18. What is the percent profit?
Q3. A volleyball sold for \$15 after a profit of 50% was added. What is the original price?

A1. \$84
A2. 60%
A3. \$10

Loss:

A loss is an amount of money subtracted from the original price.
The price minus the loss is cheaper than the original price.
The calculations for loss are the same as for discount.

Questions - Loss

Q1. A store makes a loss of 40% on fluoro-coloured socks. If the original price was \$6, what is the new price?
Q2. The original price of storm-damaged plants was \$80. If they sold for \$60, what was the percent profit?
Q3. Retro-style flared trousers sold for \$15. The loss was 80%. What is the original price?