4. Real Numbers & Proportional Reasoning

Virginia SOL 8 - 2020 Edition

4.02 Consumer applications of rational numbers

Lesson

There are many consumer applications of rational numbers. Some examples we will look at in this chapter include: calculating sales tax and tip, percent increase and decrease, and applications of simple interest. These are all areas where operations with rational numbers are used every day in real life.

Some other common consumer applications have to do with calculating a person's income. There are a number of different ways for a person to be paid for working. For example, we can be paid by the hour, via an annual salary, or by commission. Some jobs even include overtime pay for working beyond a 40 hour work week. Overtime is typically either 1.5 or 2 times the amount of the usual hourly wage. Below, we will review some consumer applications that relate to calculation of income.

When looking at various pay options, determining which is better requires some calculation on our part. In the example below, we will look at how to compare an hourly rate of income to an annual salary,

Neil's contract is based on a $30$30 hour working week and an hourly rate of $\$20$$20. Amelia's contract is based on an annual salary of $\$33040$$33040.

What is Neil's weekly income?

What is Amelia's weekly income (to the nearest cent)?

Who has the higher weekly income?

Amelia

ANeil

BAmelia

ANeil

BHow much higher is Amelia's weekly income compared to Neil's?

A salesperson usually earns a certain percentage of the total price of what they sell. This is called commission. In some professions a person will earn a small base salary in addition to commission, whereas in other jobs the only compensation will be commission. The example below looks at income earned by commission.

An auctioneer of artwork is paid $2%$2% of the value of a sale up to $\$500000$$500000, and $5%$5% of any amount by which the sale value exceeds $\$500000$$500000.

How much commission would she earn on a sale of $\$500000$$500000?

The auctioneer sells an artwork for more than $\$500000$$500000. If she receives commission of $\$13050$$13050, how much was the artwork sold for?

Let the amount the painting was sold for be $x$

`x`.

Now let's try some practice questions on our own.

Calculate the income earned for the following amounts of piecework:

washing $24$24 cars at $\$10$$10 per car

baking $26$26 croissants at $\$7$$7 per croissant

sewing $84$84 shirts at $\$8$$8 per shirt

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?

A pair of socks costs a salesman $\$1.69$$1.69 to make and he is taxed $25%$25% of the profit he makes from the sale.

If he sells each pair of socks at $\$P$$

`P`, write an expression in terms of $P$`P`for his after-tax profit per pair of socks.If the salesman wishes to make an after-tax profit of $33%$33%, calculate the price, $\$P$$

`P`, to the nearest cent, at which he must sell each pair of socks.

Solve practical problems involving consumer applications