Commission on a House Sale

A real estate agent sells a house for 250,000 dollars. Her commission rate is 3%. How much commission does she earn?

Write the rate as a decimal: $3\% = \frac{3}{100} = 0.03$ = $0.03$

Multiply the rate by the sales: $0.03 \times 250{,}000 = 7{,}500$ = $7{,}500$

Check with 1%: $1\%$ of $250{,}000$ is $2{,}500$, and $3 \times 2{,}500 = 7{,}500$ = Same answer

Answer: The agent earns a commission of **7,500 dollars**.

Base Salary Plus Commission

A car salesperson earns a base salary of 1,800 dollars a month plus 2% of his sales. This month he sold cars for 60,000 dollars. What are his total earnings?

Write the rate as a decimal: $2\% = 0.02$ = $0.02$

Find the commission: $0.02 \times 60{,}000 = 1{,}200$ = Commission: $1{,}200$

Add the base salary: $1{,}800 + 1{,}200 = 3{,}000$ = $3{,}000$

Answer: His total earnings this month are **3,000 dollars**.

Finding the Commission Rate

A shop assistant earned 270 dollars of commission on sales of 4,500 dollars. What is her commission rate?

Write the equation: $\text{rate} \times 4{,}500 = 270$ = Rate is unknown

Divide the commission by the sales: $\text{rate} = \frac{270}{4{,}500} = 0.06$ = $0.06$

Write the decimal as a percent: $0.06 \times 100\% = 6\%$ = $6\%$

Answer: Her commission rate is **6%**.

Sales Needed for a Target Income

A salesperson earns a base salary of 1,200 dollars a month plus 5% commission. How much must he sell to earn 2,500 dollars this month?

Find how much must come from commission: $2{,}500 - 1{,}200 = 1{,}300$ = Commission needed: $1{,}300$

Write the equation: $0.05 \times \text{sales} = 1{,}300$ = Sales is unknown

Divide by the rate: $\text{sales} = \frac{1{,}300}{0.05} = 26{,}000$ = $26{,}000$

Check: $1{,}200 + 0.05 \times 26{,}000 = 1{,}200 + 1{,}300 = 2{,}500$ = Correct

Answer: He must sell **26,000 dollars** worth of goods.

Tiered Commission

A company pays 5% commission on the first 10,000 dollars of sales and 8% on every dollar above 10,000. An employee sells 15,000 dollars. What is the commission?

Split the sales into the two tiers: First tier: $10{,}000$. Above: $15{,}000 - 10{,}000 = 5{,}000$ = $10{,}000$ and $5{,}000$

Commission on the first tier: $0.05 \times 10{,}000 = 500$ = $500$

Commission on the part above 10,000: $0.08 \times 5{,}000 = 400$ = $400$

Add the two parts: $500 + 400 = 900$ = $900$

Answer: The commission is **900 dollars** (not $0.08 \times 15{,}000 = 1{,}200$, because the 8% only applies above 10,000).

Mistake: Multiplying by the percent number: $3 \times 250{,}000 = 750{,}000$

Why: 3% means 3 out of 100, not 3 whole times. The commission can never be bigger than the sales.

Correct: Write the rate as a decimal first: $0.03 \times 250{,}000 = 7{,}500$

Mistake: Giving only the commission when the question asks for total earnings

Why: Total earnings include the base salary. The commission is only the extra part.

Correct: Total earnings = base salary + commission: $1{,}800 + 1{,}200 = 3{,}000$

Mistake: Using the higher tier rate on all sales: $0.08 \times 15{,}000 = 1{,}200$

Why: In tiered commission each rate applies only to its own part of the sales.

Correct: Split the sales: $0.05 \times 10{,}000 + 0.08 \times 5{,}000 = 500 + 400 = 900$

Mistake: Forgetting to subtract the base salary when finding the sales needed: $\frac{2{,}500}{0.05} = 50{,}000$

Why: Only the part of the income above the base salary has to come from commission.

Correct: First subtract: $2{,}500 - 1{,}200 = 1{,}300$, then $\frac{1{,}300}{0.05} = 26{,}000$

Real Estate Agents

When a house is sold, the agent who helped sell it is paid a percent of the selling price.

On a 400,000 dollar apartment with a 2% commission, the agent earns $0.02 \times 400{,}000 = 8{,}000$ dollars.

Comparing Job Offers at a Car Dealership

Sales jobs often mix a fixed base salary with commission. A higher base is safer, a higher rate pays more when sales are good.

Offer A pays 2,000 dollars plus 3%, offer B pays 1,400 dollars plus 5%. They pay the same when $0.02 \times \text{sales} = 600$, so at sales of 30,000 dollars. Above that, offer B pays more.

A Shop Assistant's Sales Goal

Shop assistants who earn commission often set a monthly sales target so they reach the income they need.

With a base of 1,500 dollars and 4% commission, sales of 20,000 dollars give $1{,}500 + 800 = 2{,}300$ dollars (see the bar chart).

Q: Is commission the same as a bonus?

A: Not quite. Commission is tied to each sale and grows with every dollar sold. A bonus is usually a fixed extra amount paid for reaching a goal.

Q: Can a commission rate be more than 100%?

A: No. That would mean the salesperson earns more than the price of what was sold. Real rates are usually between 1% and 20%.

Q: Why do some companies use tiered commission?

A: To reward strong sellers. A higher rate above a certain amount makes every extra sale worth more, so salespeople are motivated to sell beyond the first tier.

Q: How do I know which job offer is better?

A: Compute the total earnings of each offer for the sales you expect. You can also find the break-even sales, where both offers pay the same: below it the higher base salary wins, above it the higher rate wins.