# 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 $$\35.10$$.

1. 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.

2. If you want to tip the server an additional $$20\%$$ after tax, how much would you pay in total?

3. 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

1. 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 $$\35.10+\5.27=\40.37$$.

2. 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 $$\40.37 + \8.07 = \48.44$$.

3. 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.