Problem 18 - Prealgebra

Question

Wireless Phone Bill You recently received your Verizon wireless phone bill for the month. The total monthly bill is $$ 70.52 .\( Included in that total is $$ 13.27\) in surcharges and taxes. What percent of your wireless bill goes towards surcharges and taxes? Round your answer to the nearest tenth of a percent.

Step-by-Step Solution

Answer

18.8% of the wireless phone bill goes towards surcharges and taxes.

Step 1: Identify the Total Amount

Start by identifying the total wireless phone bill amount, which is given as \(\$70.52\).

Step 2: Determine the Surcharges and Taxes

The surcharges and taxes included in the bill are \(\$13.27\).

Step 3: Calculate the Percentage

Use the formula to calculate the percentage of surcharges and taxes:\[\text{Percentage} = \left( \frac{\text{Surcharges and Taxes}}{\text{Total Bill}} \right) \times 100 = \left( \frac{13.27}{70.52} \right) \times 100\]

Step 4: Perform the Calculation

Calculate the division first:\[\frac{13.27}{70.52} \approx 0.1882\]Then, calculate the percentage:\[0.1882 \times 100 \approx 18.82\]

Step 5: Round the Result

Round the result to the nearest tenth of a percent, giving:\(18.8\%\).

Key Concepts

Basic Arithmetic

Arithmetic skills are the foundational techniques necessary to solve a wide range of problems, including those involving percentages. To find percentages, one must begin with basic arithmetic operations such as division and multiplication. For instance, when figuring out what portion of a wireless bill is surcharges and taxes, we first divide the surcharges and taxes amount by the total bill amount. This gives us a decimal. Let's take the values from the exercise: dividing \(13.27\) by \(70.52\) results in approximately \(0.1882\). Conversion of this decimal into a percentage requires multiplication by 100, which transforms \(0.1882\) into \(18.82\). This progression from basic division to the multiplication by 100 is the essence of calculating percentages. By comprehending and practicing these steps, you're using the power of basic arithmetic to break down more complex financial tasks into simpler, manageable parts.

Surcharges and Taxes

When you look at a bill, you might notice specific portions allocated to surcharges and taxes. These are additional charges imposed on the basic costs of a service. Surcharges often cover extra costs like service fees or equipment charges, while taxes are required governmental fees. In the context of a phone bill, these can significantly impact the total amount you pay monthly. To find out their role in the total bill using percentages, as shown in the given problem, you first need to know the exact surcharges and taxes amount. Once you have this, you can calculate how much of your bill goes toward these fees by dividing this amount by the total bill, converting the result into a percentage, giving a clear picture of the additional financial burden these fees represent. Understanding surcharges and taxes helps in managing and budgeting your finances better.

Rounding Percentages

Rounding is a mathematical technique used to simplify numbers, making them easier to understand and use in communication. After you have converted a decimal to a percentage, the next potential step is rounding. Rounding a percentage can help make the number more manageable and easier to understand at a glance. In our problem, the percentage calculated was \(18.82\). This number can be awkward to read or use. Thus, rounding it to the nearest tenth of a percent simplifies it to \(18.8\%\).To round a percentage to the nearest tenth:

• Look at the digit in the hundredths place (second digit after the decimal point).
• If it is 5 or more, round the value in the tenths place up by one.
• If it is less than 5, keep the tenths place as is.

In \(18.82\), the hundredths digit is 2 (less than 5), so the tenths digit remains 8. Rounding helps provide a clean, straightforward figure that is quickly communicated and understood.