- Solve equations involving percents
A common application of percentages is figuring out how much to tip at a restaurant. Let’s consider a scenario where we calculate a tip based on a percentage of the total bill.
Aolani and her friends enjoy dinner at a restaurant, and their total bill comes to [latex]$80[/latex]. They decide to leave a [latex]20\%[/latex] tip for the excellent service they received. How do we calculate the tip amount using percentages?
To solve this we need to use the percent formula.
percent formula
The percent formula is a mathematical way to find a part of a whole. The formula is:
[latex]\text{Amount } = \frac{\text{Percent}}{100} \times \text{ base}[/latex]
where:
- Amount is the part of the base we’re trying to find (in this case, the tip).
- Percent is the percentage we want to calculate (the tip percentage).
- Base is the whole amount we’re taking a percentage of (the total bill).
To solve this, we want to find what amount is [latex]\text{20%}[/latex] of [latex]\text{\$80}[/latex]. The base is the total bill amount. For Aolani’s dinner, this is [latex]$80[/latex]. The percent is the tip rate they wish to leave. Aolani and her friends are leaving a [latex]20\%[/latex] tip. To use the percent formula, we need to convert the percentage to a decimal. We do this by dividing the percent by [latex]100[/latex].
[latex]\frac{20}{100} = .20[/latex]
Now, we use the formula to calculate the amount of the tip.
[latex]\begin{array}{l} \text{Amount} = \frac{\text{Percent}}{100} \times \text{base} \\ \text{Amount} = 0.20 \times 80 \\ \text{Amount} = 16 \\ \end{array}[/latex]
Therefore, a [latex]20\%[/latex] tip on an [latex]$80[/latex] restaurant bill comes out to [latex]$16[/latex].
Using the percent formula is a simple and effective way to calculate a percentage of any amount. Whether you’re dining out with friends or figuring out a sale discount, remember the formula [latex]\text{Amount } = \frac{\text{Percent}}{100} \times \text{ base}[/latex] to find your answer quickly and accurately.
