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Kirima offered to pay the bill and tip at a restaurant where she and her freinds had dinner. In total she paid $\$150\text{,}$ which made the tip come out to a little more than $19\%\text{.}$ We’d like to know what was the bill before tip. Set up an equation for this situation.

Use x for any variable you define and use.

Solution

A common mistake is to translate a question like this into “what is $19\%$ of $\$150\text{?}$ ” as a way to calculate the tip amount, and then subtract that from $\$150\text{.}$ But that is not how tipping works. The tip percentage is applied to the original bill, not the final total. If we let $x$ represent the original bill, then:

$\begin{aligned} \pinover{x}{bill}\pinover{+}{plus}\pinover{0.19}{19\%}\pinover{\cdot}{of}\pinover{x}{bill}\amp\pinover{=}{is}\pinover{150}{\$150} \end{aligned}$