### Let’s Think About It

From a restaurant menu, five students ordered the burger special which costs $12.95 each but includes a drink, and a dessert. The total bill included sales tax of 7% and an 18% tip. How much was the total bill?

In this concept, you will learn to find retail prices given wholesale, markups and sales tax.

### Guidance

In most things you purchase, percent is used in one way or another to calculate a final price, a discount, tax or a tip. Your understanding of this is important in making sure that you get charged the right price.

Let’s start by looking at wholesale prices and markups.

Most companies are in business to make a profit, and generally offer goods or services or both. Stores that sell you products like hairspray, potato chips, and video games, buy those products from other companies that make them and because they buy so many of the same products, store owners get special prices called **wholesale prices**. Store owners then figure out how much each piece or unit costs them and they charge you a certain amount more for each product, this is the **retail price**. The difference is called the **gross profit**. After they pay all of their other expenses, like wages, utility bills, insurance, etc., they hope to have some money left over. This is their **profit**.

Companies have to study the market and their true costs in order to calculate the best price to charge to remain competitive but still make a profit. After studying the market, they decide on a **markup**—a percent by which they will increase the wholesale price to get the retail price.

Let’s look at an example.

Let’s suppose a company sells toothpaste. They buy the toothpaste for $1.10 per tube; this is the wholesale price. They buy a case of 200 tubes all at once. In order to make a profit, they mark the price up by 65%; this is their markup. So in order to calculate the retail price, they increase the wholesale price by 65%. What will the retail price be?

First, multiply the wholesale price by the percent increase. Remember that percent means the denominator is 100.

\begin{align*}\begin{array}{rcl} 1.10 \times \frac{65}{100} &=& \frac{71.5}{100} \\ &=& 0.715 \end{array}\end{align*}

Next, add the amount of increase to the original price.

\begin{align*}1.10+0.715= 1.815\end{align*}

The answer is 1.815.

The retail price of the toothpaste is $1.82.

On most products that you purchase, stores also charge you a **sales tax** that is a percent increase determined by the government. This money is paid to the government so that they can provide services to the people.

Let’s look at an example.

The cost of a dozen roses is $33 plus tax. Let’s suppose there is a tax of 6%. What is the total price?

First, multiply the cost by the percent of the sales tax. Remember that percent means the denominator is 100.

\begin{align*}\begin{array}{rcl} 33 \times \frac{6}{100} &=& \frac{198}{100} \\ &=& 1.98 \end{array}\end{align*}

Next, add the sales tax to the original price.

\begin{align*}33+1.98=34.98\end{align*}

The answer is 34.98.

The total cost of the roses is $34.98.

### Guided Practice

A florist gets a dozen roses for $15. They charge a markup of 120%. What is the retail price of a dozen roses?

First, multiply the wholesale price by the percent increase. Remember that percent means the denominator is 100.

\begin{align*}\begin{array}{rcl} 15 \times \frac{120}{100} &=& \frac{1800}{100} \\ &=& 18 \end{array}\end{align*}

Next, add the amount of increase to the original price.

\begin{align*}15+18=33\end{align*}

The answer is 33.

The total cost of the roses is $33.

### Examples

#### Example 1

Find the total price for $4.99 with a 5% sales tax.

First, multiply the price by the sales tax.

\begin{align*}\begin{array}{rcl} 4.99 \times \frac{5}{100} &=& \frac{24.95}{100} \\ &=& 0.2495 \end{array}\end{align*}

Next, add the sales tax to the original price.

\begin{align*}4.99+0.2495=5.2395\end{align*}

The answer is 5.2395.

The total cost is $5.24.

#### Example 2

Find the total price for $25.65 with a 15% gratuity or tip.

First, multiply the price by the tip.

\begin{align*}\begin{array}{rcl} 25.65 \times \frac{15}{100} &=& \frac{384.75}{100} \\ &=& 3.8475 \end{array}\end{align*}

Next, add the amount of the tip to the original price.

\begin{align*}25.65+3.8475=29.4975\end{align*}

The answer is 29.4975.

The total cost of the roses is $29.50.

#### Example 3

Find the total price for $345.50 with a 10% markup.

First, multiply the price by the percent markup.

\begin{align*}\begin{array}{rcl} 345.50 \times \frac{10}{100} &=& \frac{3455}{100} \\ &=& 34.55 \end{array}\end{align*}

Next, add the amount of increase to the original price.

\begin{align*}345.50+34.55=380.05\end{align*}

The answer is 380.05.

The total cost of the roses is $380.05.

### Follow Up

Remember those hungry students?

Each student ordered the special, which costs $12.95. There was also sales tax of 7% and a tip of 18%.

First, find the total bill before taxes and tip for the 5 students.

\begin{align*}12.95 \times 5= 64.75\end{align*}

Next, multiply the total price by the sales tax.

\begin{align*}\begin{array}{rcl} 64.75 \times \frac{7}{100} &=& \frac{453.25}{100} \\ &=& 4.5325 \end{array}\end{align*}

Next, multiply the total price by the percent tip.

\begin{align*}\begin{array}{rcl} 64.75 \times \frac{18}{100} &=& \frac{1165.5}{100} \\ &=& 11.655 \end{array}\end{align*}

Next, add the tip and sales tax to the original price.

\begin{align*}64.75+4.5325+11.655=80.9375\end{align*}

The answer is 80.9375.

The total cost of the meal is $80.94.

### Video Review

https://www.youtube.com/watch?v=yFaa2CMx9rk&feature=youtu.be

### Explore More

Calculate the retail price given the wholesale price and percent markup.

1. Wholesale price: $6.43 markup: 38%

2. Wholesale price: $612.00 markup: 70%

3. Wholesale price: $.22 markup: 55%

Find the total cost after adding the tax.

4. Retail price: $76.50 tax: 8%

5. Retail price: $399 tax: 4.75%

6. Retail price: $8.79 tax: 7.25%

7. Retail price: $44.56 tax: 5%

8. Retail price: $345.00 tax: 11%

Find the total cost after computing the wholesale price and the tax.

9. wholesale price: $4.15 markup: 10% tax: 6%

10. wholesale price: $116.21 markup: 33% tax: 5.5%

11. wholesale price: $51.55 markup: 61.3% tax: 3.75%

12. wholesale price: $24.25 markup: 40% tax: 6%

13. wholesale price: $44.15 markup: 30% tax: 6%

14. wholesale price: $125.75 markup: 50% tax: 6%

15. wholesale price: $150.00 markup: 80% tax: 6%