Problem 17 - Prealgebra

Question

Phone Bill You recently received your monthly phone bill for service in your local area. The total of the bill was $$ 53.35 .\( You pay $$ 14.36\) in surcharges and federal and local taxes. What percent of your phone bill is made up of surcharges and taxes? Round your answer to the nearest tenth of a percent.

Step-by-Step Solution

Answer

Approximately 26.9% of the phone bill is made up of surcharges and taxes.

Step 1: Identify the Total Bill Amount

The total phone bill is given as \( \$ 53.35 \). This amount includes all charges and taxes.

Step 2: Identify the Surcharge and Tax Amount

The total surcharges and federal and local taxes amount to \( \$ 14.36 \). This is the part of the bill that we want to determine as a percentage of the total bill.

Step 3: Calculate the Percentage of the Bill Comprised of Taxes and Surcharges

To find what percent \( \\( 14.36 \) is of \( \\) 53.35 \), use the formula: \( \text{Percentage} = \left( \frac{\text{Part}}{\text{Whole}} \right) \times 100 \). Substituting the values, we get:\[\text{Percentage} = \left( \frac{14.36}{53.35} \right) \times 100\]Calculate the quotient and then multiply by 100.

Step 4: Perform the Calculation

First, divide \( 14.36 \) by \( 53.35 \):\[\frac{14.36}{53.35} \approx 0.2692\]Next, multiply \( 0.2692 \) by 100 to convert it to a percentage:\[0.2692 \times 100 = 26.92\]Thus, \( 14.36 \) is approximately \( 26.92\% \) of \( 53.35 \).

Step 5: Round to the Nearest Tenth

Finally, round \( 26.92\% \) to the nearest tenth of a percent, giving \( 26.9\% \).

Key Concepts

Understanding Surcharges and Taxes

When dealing with bills, it's common to see additional charges labeled as surcharges and taxes. Surcharges are extra fees added to your bill that cover government-imposed or company-specific costs. Taxes, on the other hand, are mandatory financial charges imposed by governments on goods and services.

Both surcharges and taxes increase your total payment. Understanding how much of your bill is due to these charges helps you to better manage your expenses. In the phone bill example given, you pay $14.36 in surcharges and taxes from a total bill of $53.35. Finding out what percentage this amount is of the total helps you assess the impact of these additional costs on your overall expenses.

Rounding to the Nearest Tenth

Rounding numbers makes them easier to understand and use in further calculations. In our example, after calculating the percentage of the bill that surcharges and taxes account for, you come up with a decimal: 26.92%. To simplify, you round this value.

• Identify the digit in the tenths place: For 26.92, this is 9.
• Look at the digit to the right (the hundredths place): Here, it is 2.
• If this digit is 5 or more, round up the tenths place. If it's less than 5, leave the tenths place as is. In our example, you leave 9 since 2 is less than 5.

Thus, 26.92% rounds to 26.9%. Rounding simplifies your results, offering the closest approximate value and aiding in clearer communication of numbers.

Mastering Division and Multiplication

Division and multiplication are fundamental operations in mathematics, essential for solving percentage problems such as the one presented in the exercise.

To find the percentage of a part relative to a whole, you'd perform the following steps:

• First, divide the part by the whole: In this case, divide $14.36 by $53.35. This simple action tells you how much one unit of the whole is based on the part.
• The result (0.2692) is then multiplied by 100 to convert this ratio into a percentage. This step translates your division's outcome into a more familiar percentage format.

Understanding when and how to apply these operations is critical, not just in academic contexts, but also in real-life situations, such as evaluating bills, sales, and continued financial management.