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Solving Commission Applications

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Solving Commission Applications

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.

Definition: Commission

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

\(\text{commission}=\text{rate of commission}·\text{total sales}\)

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 \(\text{3%}\) commission when she sells a house. How much commission will she receive for selling a house that costs \(\text{\$260,000}?\)

Solution

Identify what you are asked to find.What is the commission?
Choose a variable to represent it.Let \(c=\) the commission.
Write a sentence that gives the information to find it.The commission is 3% of the price.
Translate into an equation.Solving Commission Applications
Simplify.Solving Commission Applications
Change to percent form.Solving Commission Applications
Check. Is this answer reasonable? 
Yes. 1% of \$260,000 is \$2,600, and \$7,800 is three times \$2,600. 
Write a complete sentence that answers the question.Helene will receive a commission of $7,800.

Example

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

Solution

Identify what you are asked to find.What is the rate of commission?
Choose a variable to represent it.Let \(r=\) the rate of commission.
Write a sentence that gives the information to find it.The commission is what percent of the sale?
Translate into an equation.Solving Commission Applications
Divide.Solving Commission Applications
Simplify.Solving Commission Applications
Change to percent form.Solving Commission Applications
Check if this answer is reasonable. 
Yes. A 10% commission would have been \$145.
The 6% commission, \$87, is a little more than half of that.
 
Write a complete sentence that answers the question.The commission was 6% of the price of the stove.

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