We've already looked at commissions and other sources of income in earlier chapters. Now we are going to build on our knowledge and look at some more money terms.

Gross income: a person's income from all sources (e.g. wage, dividends and rental income) before any tax or deductions.

Net income: a person's income after tax and deductions.

Retainer: a wage earned for a predetermined amount of time or work. People who work on commission often receive a small retainer to ensure they receive a base amount for the hours that they work. e.g. Shirley receives a $\$1500$$1500 retainer per week plus a $5%$5% commission on all sales she makes. This means Shirley earns a fixed amount of $\$1500$$1500 per week plus a varying amount that is dependent on how much she sells.

Let's use these new terms to help us solve some more questions involved different types of income.

Examples

Question 1

If a commission of $20%$20% is paid on all sales, what is the total value of sales if the gross income is $\$238$$238?

Question 2

James is paid a monthly retainer of $\$800$$800 and a commission of $2%$2% of the value of the products he sells. Calculate his gross income if his sales for the month are $\$261000$$261000:

Question 3

Maria is paid a retainer of $\$240$$240 per week plus a commission based on her weekly sales. In one week she sells $\$9900$$9900 worth of goods. If her total pay for the week was $\$438$$438, what commission rate is Beth paid?

Let $x$x be her commission rate and give your answer as a percentage.

Think: How do we write an algebraic expression that describes how Maria's pay was calculated?

Do:

$240+9900x$240+9900x

$=$=

$438$438

(subtract $240$240 from both sides)

$9900x$9900x

$=$=

$198$198

(divide both sides by $9900$9900)

$x$x

$=$=

$0.02$0.02

$x$x

$=$=

$2%$2%

This means Maria is paid a $2%$2% commission rate.