topic badge

4.04 Sales tax, commissions and tips

Introduction

Other ways that percentages are commonly used are when calculating the proper tip to leave the waitstaff at a restaurant, calculating the amount of sales tax we will need to pay for purchasing an item, and finding the amount of commission paid to an employee based on how much they sell. Let's look at how to find each of these using what we've learned about  percent increase  .

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. 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. Let's look at an example.

Examples

Example 1

Sharon has finished her meal at a restaurant, but received bad service. She will only be leaving a 10\% tip. Help her calculate the tip if the meal, before sales tax, came to \$36.60.

Worked Solution
Create a strategy

Find 10\% of \$36.60.

Apply the idea
\displaystyle \text{Tip}\displaystyle =\displaystyle 36.60 \times 10\% Multiply 36.60 by 10\%
\displaystyle =\displaystyle 36.60 \times \dfrac{10}{100} Convert the percentage to a fraction
\displaystyle =\displaystyle \$3.66 Evaluate
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.

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 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 Indiana is 7\%.

a

Calculate how much tax you need to pay on a dress if it costs \$40.60 before tax.

Worked Solution
Create a strategy

Find 7\% of \$40.60 by

Apply the idea
\displaystyle \text{Tax}\displaystyle =\displaystyle 40.60 \times 7\% Multiply 40.60 by 7\%
\displaystyle =\displaystyle 40.60 \times \dfrac{7}{100} Convert the percentage to a fraction
\displaystyle =\displaystyle \dfrac{284.2}{100} Evaluate the multiplication
\displaystyle =\displaystyle 2.84 Evaluate the division

The amount of tax needed to pay is \$2.84.

b

Find the total amount to pay for the dress.

Worked Solution
Create a strategy

Add the cost of the dress 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 dress 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 \times \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.

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 3

Han is paid a commission of 3\% of the value of trucks sold in excess of \$2100. Calculate his income if he sells trucks to the value of \$6600.

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 6600-2100Subtract 2100 from sales of 6600
\displaystyle =\displaystyle 4500Evaluate
\displaystyle \text{Commission}\displaystyle =\displaystyle 4500\times \dfrac{3}{100}Convert 3\% to fraction and multiply to amount earned
\displaystyle =\displaystyle \dfrac{13500}{100}Evaluate the multiplication
\displaystyle =\displaystyle 135Evaluate the division

Han gets a commission of \$135.

Idea summary

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

Outcomes

7.RP.A.3

Use proportional relationships to solve multistep ratio and percent problems.

7.EE.B.3

Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies.

What is Mathspace

About Mathspace