Commissions
What is a commission? People earn a commission when they earn a percentage of what they sell. Many professionals (e.g., realtors, salespeople, mortgage brokers, etc.) work on commission. Every time they make a sale, they get some percent of the sale prices as their salary. That percentage that they earn is a commission.
How do you calculate a commission?
Someone might say that his commission is 4% of the sales price.
Remember that in math, "of" means multiplication, so you wan to multiply 4% times the sales price. Let's say the sales price was $500:
$$\eqalign{4\text{%} \times 500 &= \text{commission}\\.04 \times 500 &= \text{commission} &&\text{Turn percent into a decimal}\\.04\times 500 &= 20 &&\text{Multiply to find the commission is \$20}}$$
Essentially, the formula for calculating commission is: $\text{commission percent} \times \text{sales price} = \text{commission amount}$
Commission problems are usually word problems. Let's try a few:
Example: A salesperson earns a 2% commission on every sale. She sells $678 dollars in clothes over the weekend. What is her commission?
$$\eqalign{\text{commission percent} \times \text{sales price} = \text{commission amount}\\2\text{%} \times 678 &= \text{commission amount}\\.02 \times 678 &= \text{commission amount} &&\text{Turn percent into a decimal}\\.02\times 678 &= 13.56 &&\text{Multiply to find the commission is \$13.56}}$$
You might also get a problem that gives you the commission and asks you to find the sales price. You will use the same formula.
Example: A realtor earns 7% commission when he sells a house. If he earned a commission of $4000, what was the sale price of the house?
$$\eqalign{\text{commission percent} \times \text{sales price} = \text{commission amount}\\7\text{%} \times x &= \text{4000}\\.07 \times x &= \text{4000} &&\text{Turn percent into a decimal}\\\dfrac{.07x}{.07} &= \dfrac{4000}{.07} &&\text{Divide each side by .07 to find x}\\x&=57,142.90&&\text{The house cost \$57,142.90}}$$
Overall, a commission is just a percent, treat commission word problems like you would treat any other kind of percent word problem.
Practice Problems:
Percents: Commissions
1. Bella receives 8% commission on jewelry sales. Last month, her total sales were \$2000. Find her commission.
2. Your brother works part-time at Best Buy. His weekly salary is \$100 plus an 8% commission on his total sales. What is his salary for a week when his total sales are $400?
3. James receives a 15% commission on magazine subscription sales. Last week, his total sales were \$1080. Find his commission.
4. Kaitlin, a well-known real estate agent, earns 15% commission when she sells a house. If she earned a commission of $142,500, what was the sale price of the house?
5. Sunny earns a base salary of \$400 every week with an additional 7% commission on everything he sells. If Sunny sold \$5,500 worth of items last week, what was his total pay?
6. Gean earns a base salary of \$50 every week with an additional 11% commission on everything he sells. If Gean sold \$3850 worth of items last week, what was his commission? What was his total pay for the week?
7. Sara receives 13% commission on car sales. If last month her total sales were \$250,000 what was her commission for the month?
8. A real estate agent makes 4% commission on property she sells. Find her commission for selling a house that costs \$342,000.
9. Javier works at a nearby Game Stop. He makes a commission of 5% on everything he sells. If he sells 3 video games for \$115, how much money does Javier make in commission?
10. A car salemen earns 6% commission when he sells a car. If he earned a commission of \$900, what was the sale price of the car?
11. Gala makes money by commission rates. She gets 21% of everything she sells. If Gala sold \$27,000, worth of items this month, what is her salary for the month?
12. Tiffani makes a base monthly salary of \$1500. As a vendor, she must sell \$20,000 worth of items per month. She also makes a 4% commission on all sales beyond the monthly quota. If Tiffani sold \$26,000 worth of items this month, what is her total salary for the month?
Answer Key: