Percent means "per 100" or "of each hundred." In other words, a percent is a value divided by 100 or a ratio out of 100. There are many real-life uses for finding the percentage. Real estate agents, car dealers, and pharmaceutical sales representatives earn commissions that are a percentage, or part, of sales. For example, a real estate agent might earn a portion of the selling price of a house that she helps a client purchase or sell. A car salesperson earns a portion of the selling price of an automobile that she sells. Working real-life percentage problems can help you better understand the process.

## Calculating Commissions

Noel, a real estate agent, aims to earn at least $150,000 this year. She earns a 3 percent commission on every house she sells. What's the total dollar amount of houses that she must sell to reach her goal?

Start the problem by defining what you know and what you seek to determine:

- Noel will earn $3 per $100 in sales.
- She will earn $150,000 per (what dollar amount) in sales?

Express the problem as follows, where "s" stands for total sales:

3/100 = $150,000/s

To solve the problem, cross multiply. First, write the fractions vertically. Take the first fraction's numerator (top number) and multiply it by the second fraction's denominator (bottom number). Then take the second fraction's numerator and multiply it by the first fraction's denominator, as follows:

3 x s = $150,000 x 100

3 x s = $15,000,000

Divide both sides of the equation by 3 to solve for s:

3s/3 = $15,000,000/3

s = $5,000,000

So, to make $150,000 in annual commission, Noel would have to sell houses that total $5 million.

## Leasing Apartments

Ericka, another real estate agent, specializes in leasing apartments. Her commission is 150 percent of her client's monthly rent. Last week, she earned $850 in commission for an apartment that she helped her client to lease. How much is the monthly rent?

Start by defining what you know and what you seek to determine:

- $150 per $100 of the monthly rent is paid to Ericka as a commission.
- $850 per (what amount) of the monthly rent is paid to Ericka as a commission?

Express the problem as follows, where "r" stands for the monthly rent:

150/100 = $850/r

Now cross multiply:

$150 x r = $850 x 100

$150r= $85,000

Divide both sides of the equation by 150 to solve for r:

150r/150=85,000/150

r = $566.67

So, the monthly rent (for Jessica to earn $850 in commission) is $556.67.

## Art Dealer

Pierre, an art dealer, earns 25 percent commission of the dollar value of art he sells. Pierre earned $10,800 this month. What was the total dollar value of the art that he sold?

Start by defining what you know and what you seek to determine:

- $25 per $100 of Pierre's art sales is paid to him as commission.
- $10,800 per (what dollar amount) of Pierre's art sales is paid to him as commission?

Write the problem as follows, where "s" stands for sales:

25/100 = $10,800/s

First, cross multiply:

25 x s = $10,800 x 100

25s = $1,080,000

Divide both sides of the equation by 25 to solve for s:

25s/25 = $1,080,000/25

s = $43,200

Thus, the total dollar value of the art that Pierre sold is $43,200.

## Car Salesperson

Alexandria, a salesperson at a car dealership, earns 40 percent commission of her luxury vehicle sales. Last year, her commission was $480,000. What was the total dollar amount of her sales last year?

Define what you know and what you seek to determine:

- $40 per $100 of the car sales is paid to Ericka as a commission.
- $480,000 per (what dollar amount) of the car sales is paid to Ericka as a commission?

Write the problem as follows, where "s" stands for car sales:

40/100 = $480,000/s

Next, cross multiply:

40 x s = $480,000 x 100

40s = $48,000,000

Divide both sides of the equation by 40 to solve for s.

40s/40 = $48,000,000/40

s = $1,200,000

So, the total dollar amount of Alexandria's car sales last year was $1.2 million.

## Agent to Entertainers

Henry is an agent for entertainers. He earns 10 percent of his clients’ salaries. If he made $72,000 last year, how much did his clients make in all?

Define what you know, and what you seek to determine:

- $10 per $100 of the entertainers' salaries is paid to Henry as a commission.
- $72,000 per (what dollar amount) of the entertainers' salaries is paid to Henry as a commission?

Write the problem as follows, where "s" stands for salaries:

10/100 = $72,000/s

Then, cross multiply:

10 x s = $72,000 x 100

10s = $7,200,000

Divide both sides of the equation by 10 to solve for s:

10s/10 = $7,200,000/10

s = $720,000

In total, Henry's clients made $720,000 last year.

## Pharmaceutical Sales Rep

Alejandro, a pharmaceutical sales representative, sells statins for a drugmaker. He earns a 12 percent commission of the total sales of the statins he sells to hospitals. If he earned $60,000 in commissions, what was the total dollar value of the drugs that he sold?

Define what you know and what you seek to determine:

- $12 per $100 of the value of the drugs is paid to Alejandro as a commission.
- $60,000 per (what dollar value) of the drugs is paid to Alejandro as a commission?

Write the problem as follows, where "d" stands for dollar value:

12/100 = $60,000/d

Then, cross multiply:

12 x d= $60,000 x 100

12d = $6,000,000

Divide both sides of the equation by 12 to solve for d:

12d/12 = $6,000,000/12

d = $500,000

The total dollar value of the drugs that Alejandro sold was $500,000.