# 5.3: CONCEPT- Total Bill Including Tip and Tax

- Page ID
- 7003

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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Jerod and a few of his friends went to the local Chinese restaurant after seeing a matinee movie. The total of the food they ordered came to $47.50. However, the restaurant also charges 6% sales tax on the total. The server has left the tip amount up to them as well. If using a credit card, how much will they pay at the restaurant’s register, including sales tax and tip?

In this concept, you will learn to find total bills involving tips and taxes.

## Finding Total Bills Involving Tips and Taxes

When calculating tips, you add the amount back to the total of the bill for the final cost of the meal. Sometimes, the tip is left in cash on the table. When this happens, you don’t have to add it to the price of the meal. However, when using a credit card, you have to add the tip to the total to be sure that the server receives his/her tip. You also have to add any taxes.

**Taxes** are monies that are collected by the government to help pay for services such as schools, libraries, roads, and police and fire protection. A sales tax is a tax assessed on an item bought in a store. The rate of sales tax is given as a percent. You can find the amount of sales tax by using the following formula:

\(\ \text{Amount of sales tax} = \text{price} \times \text{rate of sales tax}\)

After you calculate the amount of a tax using the percentage and the formula, you have to add it to an original amount. With sales tax, this is especially important.

Let’s look at an example.

Emily bought a jacket for $85. If the sales tax is 7.5%, find the total cost of the jacket.

First, find the amount of sales tax.

\(\ 7.5 \% \text{ of }\$ 85=0.075 \times \$ 85=\$ 6.375\)

You need to round $6.375 to the nearest penny, which is $6.38.

Then, add the original price of the jacket and the sales tax.

\(\ \$ 85+\$ 6.38=\$ 91.38\)

The total cost of the jacket, with sales tax, is $91.38.

Let’s look at another example.

Mr. and Mrs. Green and their four children went out to dinner. The cost of the meal was $72. The restaurant added a tip of 18% to the bill. What was the total cost of the dinner?

First, find the amount of the tip.

\(\ 18 \%\text{ of }\$ 72=0.18 \times \$ 72=\$ 12.96\)

Then, add the cost of the meal and the tip.

\(\ \$ 72+\$ 12.96=\$ 84.96\)

The total cost of the dinner, with tip, was $84.96.

### Examples

Earlier, you were given a problem about Jerod‘s restaurant bill.

The total amount of the food came to $47.50. But the restaurant also charges 6% sales tax on the total. The excellent server has left the tip amount up to them as well. If using a credit card, how much will they pay at the restaurant’s register, including sales tax and tip?

**Solution**

First, figure out the sales tax. To do this, convert the percent to a decimal and then multiply by the total cost of the meal.

\(\ 0.06 \times \$ 47.50=\$ 2.85\)

Next, figure out the tip. Because the server provided very good service, they decide to leave an 18% tip. Convert the percent to a decimal and multiply by the cost of the meal.

\(\ 0.18 \times \$ 47.50=\$ 8.55\)

Then, add it all up.

\(\ \$ 47.50+\$ 2.85+\$ 8.55=\$ 58.90\)

The answer is the total they will pay at the register with a credit card is $58.90, including the tax and tip.

Brandon bought a T-shirt for $8.99 and a pair of shorts for $11.99. If the rate of sales tax is 7%, how much did he spend in total?

**Solution**

First, find the total cost of the items purchased.

\(\ \$ 8.99+\$ 11.99=\$ 20.98\)

Next, find the amount of sales tax. In doing so, first convert the percent to a decimal and then multiply by the total cost. Round your answer to the nearest cent.

\(\ \$ 20.98 \times 0.07=\$ 1.47\text{ (Notice that you rounded up to }1.47 \)

Then, add this tax to the cost of the items.

\(\ \$ 20.98+\$ 1.47=\$ 22.45\)

The answer is the total cost of the T-shirt and shorts, with tax, is $22.45.

Find the total amount on a $65.00 item with 5% sales tax assessed.

**Solution**

First, find the amount of sales tax. In doing so, first convert the percent to a decimal and then multiply by the total cost.

\(\ \$ 65.00 \times 0.05=\$ 3.25\)

Then, add this tax to the cost of the item.

\(\ \$ 65.00+\$ 3.25=\$ 68.25\)

The answer is the total cost of the item, with tax, is $68.25.

Find the total amount of a $30.00 bill with a 20% tip.

**Solution**

First, find the amount of the tip.

\(\ 20 \%\text{ of }\$ 30=0.20 \times \$ 30=\$ 6.00\)

Then, add the cost of the meal and the tip.

\(\ \$ 30+\$ 6=\$ 36\)

The total amount of the bill, with tip, is $36.

Find the total amount of $150.00 item with a 10% sales tax assessed.

**Solution**

First, find the amount of sales tax. In doing so, first convert the percent to a decimal and then multiply by the total cost.

\(\ \$ 150.00 \times 0.10=\$ 15.00\)

Then, add this tax to the cost of the item.

\(\ \$ 150.00+\$ 15.00=\$ 165.00\)

The answer is the total cost of the item, with tax, is $165.00.

### Review

Calculate the total amount paid, including sales tax and tip, if the sales tax is 4% and a tip of 20% is given.

- Total: $56.75
- Total: $43.25
- Total: $65.00
- Total: $25.50
- Total: $18.75
- Total: $59.00
- Total: $21.50
- Total: $44.50
- Total: $12.50
- Total: $43.00
- Total: $89.50
- Total: $99.35
- Total: $235.75
- Total: $300.50
- Total: $678.25

### Review (Answers)

To see the Review answers, open this PDF file and look for section 6.19.