# Tax and Tip

Alignments to Content Standards: 7.RP.A.3

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.
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.