### Learning Outcomes

- Calculate sales commission given total purchase price and rate
- Calculate rate of commission given purchase price and commission earned

Sales people often receive a commission, or percent of total sales, for their sales. Their income may be just the commission they earn, or it may be their commission added to their hourly wages or salary. The commission they earn is calculated as a certain percent of the price of each item they sell. That percent is called the **rate of commission**.

### Commission

A commission is a percentage of total sales as determined by the rate of commission.

[latex]\text{commission}=\text{rate of commission}\cdot \text{total sales}[/latex]

To find the commission on a sale, multiply the rate of commission by the total sales. Just as we did for computing sales tax, remember to first convert the rate of commission from a percent to a decimal.

### example

Helene is a realtor. She receives [latex]\text{3%}[/latex] commission when she sells a house. How much commission will she receive for selling a house that costs [latex]\text{\$260,000}?[/latex]

Solution

Identify what you are asked to find. | What is the commission? |

Choose a variable to represent it. | Let [latex]c=[/latex] the commission. |

Write a sentence that gives the information to find it. | The commission is [latex]3\text{%}[/latex] of the price. |

Translate into an equation. | |

Simplify. | [latex]c=7800[/latex] |

Change to percent form. | [latex]r=8.5\text{%}[/latex] |

Check. Is this answer reasonable? | |

Yes. [latex]1\text{%}[/latex] of [latex]\text{\$260,000}[/latex] is [latex]\text{\$2,600}[/latex], and [latex]\text{\$7,800}[/latex] is three times [latex]\text{\$2,600}[/latex]. | |

Write a complete sentence that answers the question. | Helene will receive a commission of [latex]\text{\$7,800}[/latex]. |

### try it

In this video, we show another example of how to calculate the amount of commission earned given the rate of commission, and the amount of the sale made.

### example

Rikki earned [latex]\text{\$87}[/latex] commission when she sold a [latex]\text{\$1,450}[/latex] stove. What rate of commission did she get?

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