# How to Calculate a Tip

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• 0:03 What Is a Tip?
• 1:27 Calculating a Tip
• 3:26 Taxes and Total Cost of a Bill
• 4:30 Mental Math Calculations
• 6:29 Lesson Summary
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Lesson Transcript
Instructor: Thomas Higginbotham

Tom has taught math / science at secondary & post-secondary, and a K-12 school administrator. He has a B.S. in Biology and a PhD in Curriculum & Instruction.

Tips are quantities of money that are often added onto to the original cost of a bill. Figuring out these items is as simple as setting up a ratio between the tip percentage and the bill amount. In this lesson learn how easy it is to calculate a tip.

## What Is a Tip?

John used to have a paper route. After getting paid, he would treat himself to breakfast at a local diner every Sunday, sitting next to regulars like Red and Lefty. Betty was usually his waitress, and because she did a great job, John always tipped her well. Fortunately, he ordered the same thing most weeks, and since his mom was a math teacher, calculating the tip was easy. Perhaps he didn't realize it at the time, but John was using ratios and proportions, one of the most commonly used math practices in daily life.

When you receive a service, such as being waited on at a restaurant or having a hotel room cleaned by a housekeeper, it is often times customary to leave a tip. A tip is an amount of money given that says 'thank you' for the service. The amount of the tip is usually a percentage, or part of, the total cost of that service. In the United States, standards vary regionally, but in general, service of expected quality should merit a tip of 15% of the original bill. Poor service might merit 10%, while excellent service merits 20% or more. Making calculations on such tips uses a straightforward ratio (fraction) and proportion, meaning an equation with two ratios.

## Calculating a Tip

Fifteen percent means 15 out of 100, or the proportional equivalent. To calculate 15% using ratios and proportions, set up a simple proportion and solve, as in this example.

A trip to Happy's Diner resulted in a bill of \$45. Service was good, but not exceptional. How do you figure out the tip?

Simple, set up a proportion for 15%, or whatever percentage tip you feel the service merits.

Then cross-multiply:

15 * 45 = 100 * x

675 = 100x

\$6.75 = x

The 15% tip is \$6.75.

However, most people aren't likely to set up a proportion on a napkin at the diner. Instead, they can simply multiply the total by the decimal form of the tip percentage (for example, 10% = 0.1, 15% = 0.15, 20% = 0.2). Using the same example, calculating a 15% tip on a \$45 bill would be:

\$45 * 0.15 = \$6.75.

How would you calculate the tip for your \$45 bill at Happy's Diner if you had excellent service? Remember, if service was great, a tip of 20% may be given. In this case, twenty percent means 20 out of 100.

20 * 45 = 100 * x

900 = 100x

\$9.00 = x

Using the decimal form of 20% will get you the same amount: \$45 * 0.2 = \$9.00

## Taxes and Total Cost of a Bill

In some places, there is a meals or sales tax added on to the bill. Those taxes can vary from 1 to 9 percent. Fortunately, calculating that is as simple as calculating a tip. Incidentally, it is generally practiced that tip is calculated on the bill before tax is added. Percentages are still ratios, so setting up a proportion as before is how to figure these out. A \$45 bill with a 6% sales tax looks like this:

6 * 45 = 100 * x

270 = 100x

\$2.70 = x

6% sales tax = \$2.70

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