Problem 24 - Prealgebra

Question

Set up the following problems the same way you set up Problems 1-22. Then use a calculator to do the calculations. A homeowner had a \(\$ 95.90\) electric bill in December. In January the bill was \(\$ 107.40 .\) Find the percent increase in the electric bill from December to January. (Round to the nearest whole number.)

Step-by-Step Solution

Answer

The percent increase in the electric bill is approximately 12%.

Step 1: Identify the Known Values

First, we need to identify the known values from the problem. We have the bill for December, which is \( \\(95.90 \), and the bill for January, which is \( \\)107.40 \). We need to find the percent increase from December to January.

Step 2: Calculate the Increase in the Bill

Subtract the December bill from the January bill to find the increase. \[ \text{Increase} = 107.40 - 95.90 = 11.50 \].

Step 3: Set Up the Percent Increase Formula

The formula for percent increase is given by: \[ \text{Percent Increase} = \left( \frac{\text{Increase}}{\text{Original Amount}} \right) \times 100 \]Here, the original amount is the December bill, \( \$95.90 \).

Step 4: Plug Values Into the Formula

Plug the values into the percent increase formula to calculate:\[ \text{Percent Increase} = \left( \frac{11.50}{95.90} \right) \times 100 \]

Step 5: Perform the Calculation

Let's calculate the percentage increase:\[ \text{Percent Increase} = \left( \frac{11.50}{95.90} \right) \times 100 \approx 11.9906 \]Round this number to the nearest whole number to find the increase in percentage.

Step 6: Round to the Nearest Whole Number

Round \( 11.9906 \) to the nearest whole number to find the final result. The percent increase is approximately \( 12 \% \).

Key Concepts

Calculating Percentage

Understanding how to calculate percentages is key in many real-world applications. A percentage represents a portion of a hundred, serving as an ideal way to compare relative sizes. To find the percentage of any increase, you need to follow a simple formula. Start by calculating the difference between the two values you are comparing. In our example, we calculated the increase in the electric bill from \(95.90 in December to \)107.40 in January. The difference or increase here is \(11.50.

With this increase calculated, the percentage increase is derived using the formula:

• Percentage Increase = \( \left( \frac{\text{Increase}}{\text{Original Amount}} \right) \times 100 \)

Here, make sure to divide the increase by the original amount, which in our case is the December bill of \)95.90. Then multiply this result by 100 to convert the result into a percentage format.

Using this foundational approach helps ensure accurate percentage calculations with any set of numbers you might encounter.

Bill Comparison

Comparing bills, such as utility bills from one month to another, is an essential task for monitoring financial changes. This comparison can highlight unusual patterns or increases that might require investigation. In our exercise, the focus was on examining the electric bill differences between December and January.

By first identifying the known amounts (December's and January's bills), it becomes more straightforward to find the difference. This difference then serves as the "increase" in our percentage calculation, allowing us to directly compare the two periods using a clear numerical basis.

• For instance, understanding how changes affect your budget can guide decisions such as reducing consumption or exploring cost-saving options.
• Regular comparison of bills can also help in spotting billing errors or seasonal patterns that might otherwise go unnoticed.

Through consistent monitoring, you can stay on top of your expenses and make informed financial decisions.

Algebraic Expressions

Algebraic expressions play a significant role when dealing with mathematical operations involving variables or known quantities, such as calculating percentage increases. Here, we use basic algebraic concepts to set up and solve our problem.

The percentage increase formula can be viewed as an algebraic expression where the known values, such as the increase and original amount, substitute into the formula. In algebra, these expressions are used to simplify complex problems by breaking them down into smaller, manageable parts.

• For instance, the expression \( \frac{\text{Increase}}{\text{Original Amount}} \times 100 \) uses division and multiplication to solve for the percent increase.
• Using algebraic expressions ensures that calculations are systematic, providing a reliable method for solving similar problems consistently.

By endeavoring to understand and manipulate these expressions, students can better handle a wide variety of mathematical challenges with confidence and precision.