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# 6.18: Estimating Tips

Difficulty Level: At Grade Created by: CK-12
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Shen and his family went to a restaurant to celebrate his last day of school. When the bill arrived the total came to $45.20. Shen knows they are supposed to leave a tip on the total amount. How much of a tip should they leave and what is the total amount of the bill including the tip? In this concept, you will learn to estimate appropriate tips. ### Estimating Tips A tip is an amount of money that is given to a worker, such as a waiter or luggage handler, who performs a service for you. A common tip amount is 15% of the cost of the meal or other service. Since you don’t usually calculate a tip exactly, you can estimate the amount of a tip. Follow these steps to estimate a 15% tip: First, round the total bill to the nearest whole dollar amount. Next, find 10% of this amount by moving the decimal point one place to the left. Now, find half of the amount you found in Step 2. This will give you 5% of the total cost. Then, add the 10% amount and the 5% amount together. This will give you your total tip. Let’s apply these steps by taking a look at an example. Estimate a 15% tip on a meal that costs$29.75.

First, round $29.75 to$30.

Next, find 10% of $30=$3.00\begin{align*}30 = 3.00\end{align*}

Now, find half of 10%: Half of $3.00=$1.50\begin{align*}3.00 = 1.50\end{align*}

Then, add 10% and 5%: $3.00+$1.50=4.50\begin{align*}3.00 + 1.50 = 4.50\end{align*} A 15% tip on a meal that costs29.75 is about $4.50. Let’s take a look at another example. A tip doesn’t always have to be 15%. It can be more or less depending on the level of service you received. If your waitress was especially good you may decide to give her a bigger tip. Estimate a 20% tip on a restaurant bill of$38.95.

You can start by thinking about 10% of this bill. Since that involves simply moving the decimal point, you can say that the estimate of 10% is $3.90. Now 20% is double that to$7.80.

You can say that an estimate of a 20% tip is in a range from $7.50$8.00\begin{align*}7.50 - 8.00\end{align*}.

### Examples

#### Example 1

Earlier, you were given a problem about Shen’s end-of-school celebration meal.

The total of the family’s bill came to $45.20. How much of a tip should they leave and what is the total amount of the bill including the tip? Recall that the tip should be based on the level of service received. For good service you should leave 15%. For exceptional service, you might want to leave 20%. First, round$45.20 to $45.00. Next, find 10% of$45=4.50\begin{align*}45 = 4.50\end{align*} Now, find half of4.50=2.25\begin{align*}4.50 = 2.25\end{align*} Then, for a 15% tip add 10%+5%:4.50+$2.25=$6.75\begin{align*}10\% + 5\%: 4.50 + 2.25 = 6.75\end{align*}

Finally, for 20% double 10%: 2(4.50)=9.00\begin{align*}2(4.50) = 9.00\end{align*} The answer is Shen's family should leave a tip between6.75 and $9.00, so the total amount of their bill, including tip, is between$51.95($45.20+$6.75)\begin{align*}51.95 (45.20 + 6.75)\end{align*} and $54.20($45.20+9.00)\begin{align*}54.20 (45.20 + 9.00)\end{align*}. #### Example 2 Estimate a 20% tip on a meal that costs54.15.

Since the tip is about 20%, you can find 10% and then double it.

First, round $54.15 to$54.

Next, find 10% of $54=$5.40\begin{align*}54 = 5.40\end{align*}

Then, find 20% of $54=2×$5.40=10.80\begin{align*}54 = 2 \times 5.40 = 10.80\end{align*} A 20% tip on a meal that costs54.15 is about $10.80. #### Example 3 Estimate a 15% tip for a$29.00 bill. Provide a range in your answer.

First, $29.00 is already rounded. Next, find 10% of$29=2.90\begin{align*}29 = 2.90\end{align*} Now, find half of2.90=1.45\begin{align*}2.90 = 1.45\end{align*} Then, add 10% and 5%:2.90+$1.45=$4.35\begin{align*}2.90 + 1.45 = 4.35\end{align*}

A 15% tip on a meal whose cost is $29.00 is between$4.00 and $4.50. #### Example 4 Estimate a 15% tip for a$16.00 bill. Provide a range in your answer.

First, $16.00 is already rounded. Next, find 10% of$16=1.60\begin{align*}16 = 1.60\end{align*} Now, find half of1.60=0.80\begin{align*}1.60 = 0.80\end{align*} Then, add 10% and 5%:1.60+$0.80=$2.40\begin{align*}1.60 + 0.80 = 2.40\end{align*}

A 15% tip on a meal that costs $16.00 is between$2.00 and $2.50. #### Example 5 Estimate a 15% tip for a$55.00 bill. Provide a range in your answer.

First, $55.00 is already rounded. Next, find 10% of$55=5.50\begin{align*}55 = 5.50\end{align*} Now, find half of5.50=2.75\begin{align*}5.50 = 2.75\end{align*} Then, add 10% and 5%:5.50+$2.75=$8.25\begin{align*}5.50 + 2.75 = 8.25\end{align*}

A 15% tip on a meal that costs $55.00 is between$8.00 and $8.50. ### Review Estimate a tip of 20% for each amount. 1. A tip on$15.00
2. A tip on $28.00 3. A tip on$25.00
4. A tip on $35.00 5. A tip on$45.00
6. A tip on $50.00 7. A tip on$90.00
8. A tip on $120.00 9. A tip on$125.00
10. A tip on $110.50 11. A tip on$130.75
12. A tip on $135.50 13. A tip on$98.78
14. A tip on $89.67 15. A tip on$100.20

To see the Review answers, open this PDF file and look for section 6.18.

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