Tax and Tip

Task

After eating at your favorite restaurant, you know that the bill before tax is $52.60 and that the sales tax rate is 8%. You decide to leave a 20% tip for the waiter based on the pre-tax amount. How much should you leave for the waiter? How much will the total bill be, including tax and tip? Show work to support your answers.

Solutions

Solution: An exact answer

To figure out the tip, you need to find 20% of \$52.60. $$0.2 \times 52.6 = 10.52$$ You should leave \$10.52 for the waiter if you want to leave him exactly 20%.

To figure the tax, you need to find 8% of \$52.60. $$0.08\times 52.6 = 4.208$$ Next, add them up: $$52.6 + 10.52 + 4.208 = 67.328$$ The total bill, including tax and tip, will be \$67.33.

Solution: Estimating an answer

If you are not concerned whether you give the waiter exactly 20%, you can simply estimate the total bill. Tax and tip together are a little less than 30% and the bill is a little more than \$50. Since 30% of 50 is 15, the tax and tip together are approximately \$15. (Note that the exact calculation is \$14.73.)

We can also estimate the total bill as \$52 + \$15 = \$67, which is very close to the exact calculation of \$67.33. This kind of estimating is a good way to check the answer to an exact calculation, and more like the way you would probably compute tax and a tip in a real restaurant.

Solution: Exact tax, approximate tip

In a real-world context, restaurant patrons generally estimate the tip, but pay the exact tax based on the calculation of their bill. Therefore, a third solution possibility is for students to estimate the tip portion of the calculations and to find the exact tax when calculating the total bill.

If you wish to estimate the tip, you can round \$52.60 to \$50. Twenty percent of \$50 is \$10. So, you would leave a \$10 tip.

To figure tax, you need to find 8% of \$52.60: $$0.08 \times 52.6 = 4.208.$$ Next, add the estimated tip, the calculated tax, and the pre-tax bill: $$52.60 + 10 + 4.208 = 66.808.$$ The total bill will be \$66.81.