You’ve just enjoyed a delicious meal at a restaurant with your friend. The cost of the meal before tax and tip was \(\$35.10\).
Suppose the tax is \(15\%\) of the total cost. Estimate the dollar amount of tax using a mental math strategy. Then calculate the actual dollar amount of tax, and total cost including tax.
If you want to tip the server an additional \(20\%\) after tax, how much would you pay in total?
How much change would you receive if you paid with a \(\$100\) bill?
Extension: Suppose you are a server. In general, when would you rather receive a \(\$20\) tip instead of \(20\%\) of your bill? Justify your thinking.
To estimate the dollar amount of tax, we could first round the total cost to \(\$35\). Then we could think of \(15\%\) as \(10\% + 5\%\). Since \(10\%\) of \(\$35\) is \(\$3.50\), and half of that is \(\$1.75\), we can estimate that the dollar amount of tax is \(\$3.50 + \$1.75 = \$5.25\).
The actual dollar amount of tax is \(\$35.10\times 0.15=\$5.265\), which rounds to \(\$5.27\). Thus, the total cost including tax is \(\$35.10+\$5.27=\$40.37\).
If you want to tip the server an additional \(20\%\), then we need to calculate \(20\%\) of \(\$40.37\). We know that \(10\%\) of \(\$40.37\) is \(\$4.037\). We then double that to get \(20\%\), which is \(\$8.074\). Rounded to the nearest cent, this is \(\$8.07\). Finally, adding that to the total cost including tax gives \(\$40.37 + \$8.07 = \$48.44\).
If you paid with a \(\$100\) bill, your change would be \(\$100-\$48.44=\$51.56\).
Extension: When \(20\%\) of the total cost including tax is less than \(\$20\), then a \(\$20\) tip would likely be preferred. When \(20\%\) of the total cost including tax is greater than \(\$20\), then a tip of \(20\%\) would likely be preferred.