#
Problem
of the Week

Problem
B and Solution

Server
Satisfaction

## Problem

Youâ€™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.

## Solution

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.