Problem 91 - Elementary Algebra

Question

Geneva treated her parents to dinner at their favorite restaurant. The bill was \(\$ 74.25 .\) Geneva wants to leave \(16 \%\) of the total bill as a tip. How much should the tip be?

Step-by-Step Solution

Answer

The tip should be $11.88.

Step 1 - Convert Percentage to Decimal

To determine the tip amount, first convert the percentage to a decimal. Move the decimal point two places to the left: 16% = 0.16

Step 2 - Calculate the Tip Amount

Multiply the total bill by the decimal form of the tip percentage. 0.16 * \(74.25 = \)11.88

Step 3 - Verify the Calculation

Double-check the multiplication to ensure accuracy: 74.25 * 0.16 = 11.88

Key Concepts

percentage to decimal conversion

When converting a percentage to a decimal, you simply need to move the decimal point two places to the left.
This is because percentages are based on a scale of 100. To illustrate this, let's take Geneva's situation where she wants to leave a 16% tip.
Here’s how you do it:

• Start with 16%.
• Imagine a decimal point at the end of 16, like this: 16.0%
• Now, move that decimal point two spots to the left: 0.16.

So, 16% as a decimal becomes 0.16.
This is the number you will use in further calculations.

multiplying decimals

Now that we have converted the percentage to a decimal, it's time to calculate the tip amount.
In Geneva's case, she needs to multiply the total bill by 0.16.
Step-by-step, it looks like this:
\(0.16 \times 74.25 = 11.88\)
Follow these simple steps to multiply decimals:

• Ignore the decimal points initially; multiply the numbers as if they are whole numbers.
• So, you would multiply 16 by 7425.
• This gives you 118800.

Next, count the total number of decimal places in the numbers you are multiplying.
Here, 0.16 has two decimal places, and 74.25 has two decimal places, making a total of four decimal places.
Finally, put the decimal point in your answer so that it has four decimal places: 11.8800, which simplifies to 11.88. So, the tip amount Geneva should leave is \(11.88\).

verifying calculations

It's always a good idea to double-check your work to ensure your calculations are correct.
This step involves doing the multiplication again to make sure you get the same result.
Let's re-calculate Geneva's tip:
\(0.16 \times 74.25 \= 11.88\)
Once more, multiply as if they are whole numbers:
\(16 \times 7425 \= 118800\).
Add back the decimal points:
\(0.16 \) has two places, and \(74.25 \) has two, for a total of four:
\(118800 \) with four decimal places is \(11.8800,\) rounding to \(11.88\)
If both calculations match, \(11.88\), you know your answer is accurate.