Topics
1. Real Numbers
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United States of AmericaVirginia
Grade 8

1.06 Sales tax, commissions and tips

Lesson
Practice

Tips

A tip is an amount of money left for the staff, in addition to paying the bill, as a sign that we appreciate good service. The tip is typically calculated as a percentage of the bill before tax is applied.

Tips are common in the service industry, but in other sectors like government receiving a tip can be considered illegal. So, it is important to know the customary amount to tip for different services and who we should not offer a tip to.

This image below displays the tipping customs of many countries around the world. You can see that tips vary from 0 to 20\%.

An infographic on tipping ettiquete around the world. Ask your teacher for more information.

We can use what we already know about finding a percentage, to calculate the tip.

Examples

Example 1

Anasofia and her daughter have finished her meal at a restaurant and received exceptional service. She will be leaving a 25\% tip. Help her calculate the tip if the meal, before sales tax, came to \$42.30.

Worked Solution
Create a strategy

To find the tip amount, we need to calculate 25\% of \$42.30. We have to convert the decimal into a percentage and multiply by the amount of the bill.

Apply the idea
\displaystyle \text{Tip}\displaystyle =\displaystyle 42.30 \cdot 25\% Multiply 42.30 by 25\%
\displaystyle =\displaystyle 43.25 \cdot \dfrac{25}{100} Convert the percentage to a fraction
\displaystyle =\displaystyle \$10.58 Evaluate and round
Idea summary

A tip is an amount of money left for the staff, in addition to paying the bill, as a sign that we appreciate good service. It is calculated as a percentage of the bill, typically before tax is applied.

Sales tax

In most of the United States, sales tax is added on to the marked price of an item at the point of sale. This tax is an extra amount that is added to the marked price of goods or the stated price of a service.

In some countries, sales taxes is already included in the marked price ticket. So, similar to being aware of tipping customs, it is useful to know how sales tax is collected where we are making a purchase.

Sales taxes in the U.S. can range from state to state (or territory) and can be between 4\% in Guam and 12\% in Arkansas. Sometimes particular goods or services like hotels, alcohol or cigarettes may be subject to higher taxes than other items.

Examples

Example 2

The sales tax on clothing in Florida is 6\%.

a

Calculate how much tax you need to pay on a jacket if it costs \$38.20 before tax.

Worked Solution
Create a strategy

To calculate how much tax will be charged, we need to calculate 6\% of \$38.20. We have to convert the decimal into a percentage and multiply by the cost of the jacket.

Apply the idea
\displaystyle \text{Tax}\displaystyle =\displaystyle 38.20 \cdot 6\% Multiply 38.20 by 6\%
\displaystyle =\displaystyle 38.20 \cdot \dfrac{6}{100} Convert the percentage to a fraction
\displaystyle =\displaystyle \dfrac{229.2}{100} Evaluate the multiplication
\displaystyle =\displaystyle 2.29 Evaluate the division and round

The amount of tax needed to pay is \$2.29.

b

Find the total amount to pay for the jacket.

Worked Solution
Create a strategy

Add the cost of the jacket and the sales tax.

Apply the idea
\displaystyle \text{ Total cost}\displaystyle =\displaystyle \$40.60 + \$2.84Add the total cost and the tax
\displaystyle =\displaystyle \$43.44Evaluate

The total amount to pay is \$43.44.

Reflect and check

We can apply the concept of percent increase to find the total cost of the jacket including tax.

Remember that adding 7\% to \$40.60 is the same as multiplying \$40.60 by 100\% + 7\% or 107\%.

\displaystyle \text{Total cost}\displaystyle =\displaystyle 40.60 \cdot \dfrac{107}{100}Convert the percent to fraction
\displaystyle =\displaystyle \dfrac{4344.2}{100}Evaluate the multiplication
\displaystyle =\displaystyle 43.44Evaluate the division

The total amount to pay is \$43.44.

Example 3

Jaleel is at the grocery store. He added up the total of the items in his cart using the prices seen on the shelves. His current total, or the subtotal, is \$123.50. When he checks out, the total is \$133.38

a

How much did Jaleel pay in sales tax?

Worked Solution
Create a strategy

We have to find the difference in the two prices by subtracting the subtotal from the total at the checkout.

Apply the idea
\displaystyle \text{Cost of tax}\displaystyle =\displaystyle \$133.38-\$123.50Subtract the subtotal from the cost at checkout
\displaystyle =\displaystyle 9.88Evaluate

The cost of the tax is \$9.88.

b

What is the sales tax percentage?

Worked Solution
Create a strategy

We know that the total amount paid is equal to the subtotal times the tax percentage. We can substitute the price from check out and the price he calculated and solve for the missing percentage.

Apply the idea
\displaystyle \$9.88\displaystyle =\displaystyle 123.50 \cdot \dfrac{x}{100}Substitute the tax cost and the subtotal
\displaystyle \dfrac{\$9.88}{123.50}\displaystyle =\displaystyle \dfrac{\$123.50}{\$123.50} \cdot \dfrac{x}{100}Divide both sides by \$123.50
\displaystyle 0.08\displaystyle =\displaystyle \dfrac{x}{100}Evaluate the division
\displaystyle 0.08 \cdot 100\displaystyle =\displaystyle \left ( \frac{x}{100} \right ) \cdot 100Multiply both sides by 100
\displaystyle 8\displaystyle =\displaystyle xEvaluate

The tax percentage is 8\%

Idea summary

Sales tax is an amount to be paid in addition to the marked price of goods or the stated price of a service, and is added on to the marked price, at the point of sale.

Commission

A commission is a typical payment method for salespeople selling items like furniture, cars or real estate. Commission is usually paid as a percentage of an employee's total sales.

Commission payments can make up an employee's entire income, or they can be paid on top of a regular income, called a retainer.

Examples

Example 4

Alton works in a jewelry store and is paid a commission of 5.5\% of the value of jewelry sold in excess of \$1500, in addition to his monthly salary of \$3000. Calculate his monthly income if he sells \$3200 worth of jewelry this month.

Worked Solution
Create a strategy

Calculate the amount that commissions are earned on, then multiply by the percentage to find the commission.

Apply the idea
\displaystyle \text{Amount to earn commission}\displaystyle =\displaystyle 3200-1500Subtract 1500 from sales of 3200
\displaystyle =\displaystyle 1700Evaluate
\displaystyle \text{Commission}\displaystyle =\displaystyle 1700\cdot \dfrac{5.5}{100}Convert 5.5\% to fraction and multiply to amount earned
\displaystyle =\displaystyle \dfrac{9350}{100}Evaluate the multiplication
\displaystyle =\displaystyle 93.5Evaluate the division

Alton gets a commission of \$93.50.

To find his his total income, we have to add the amount of his commission to his monthly salary.

\displaystyle \text{Total income}\displaystyle =\displaystyle 3000+93.50Add his salary to his commission
\displaystyle =\displaystyle \$3093.50Evaluate the addition

Alton's total monthly income is \$3093.50

Idea summary

Commission applies the concept of percentage increase, and is paid to an employee based on how much they sell.

Outcomes

8.CE.1

The student will estimate and apply proportional reasoning and computational procedures to solve contextual problems.

8.CE.1b

Estimate and solve contextual problems that require the computation of the sales tax, tip and resulting total.

8.CE.1c

Estimate and solve contextual problems that require the computation of the percent increase or decrease.

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