# Business Percentages

## 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?

**Answer:**

Commission

= Percent Commission × Sales

= 5% of $4000

= ^{5}⁄_{100} × $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.

**Answer:**

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?

**Answer:**

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?

**Answers:**
**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?

**Answer (Long method):**

Discount

= Percent Discount × Original price

= 15% × $200

= $30

Discounted Price

= Original Price – Discount

= $200 – $30

= $170

**Answer (Short method):**
*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?

**Answer:**

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?

**Answer:**

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?

**Answers**
**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?

**Answer (Long method):**

Profit

= Percent Profit × Original price

= 35% × $20

= $7

Price with profit

= Original Price + Profit

= $20 + $7

= $27

**Answer (Short method):**
*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?

**Answer:**

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?

**Answer:**
*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?

**Answers**
**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?

**Answers**
**A1.** $3.60
**A2.** 25%
**A3.** $75