Problem 10 - Prealgebra

Question

Find the percent of change. Round to the nearest tenth, if necessary. Then state whether the percent of change is a percent of increase or a percent of decrease. from \(\$ 289\) to \(\$ 762\)

Step-by-Step Solution

Answer

The percent of change is a 163.7% increase.

Step 1: Understand the Formula

To find the percent of change, we use the formula: \[\text{Percent of Change} = \frac{\text{New Value} - \text{Original Value}}{\text{Original Value}} \times 100\%\] where the 'New Value' is 762 and the 'Original Value' is 289.

Step 2: Calculate the Difference

Subtract the original value from the new value to find the difference. This gives us: \(762 - 289 = 473\). This is the change in value.

Step 3: Compute the Change in Fraction Form

Divide the difference by the original value to get the change as a fraction: \( \frac{473}{289} \approx 1.637\).

Step 4: Convert to Percent

Multiply the fractional result by 100 to convert it to a percentage: \(1.637 \times 100\% = 163.7\%\).

Step 5: Determine Type of Change

Since the new value (762) is greater than the original value (289), this implies there is an increase. Therefore, the percent of change is a percent of increase.

Key Concepts

Understanding Percent Increase

When we talk about percent increase, we refer to how much a quantity has grown in relation to its original amount. It's a useful way to express growth or expansion in terms of percentage, which is easy for most people to understand. Here’s how you can make sense of percent increase:

• First, identify the original number or amount you start with.
• Next, note the new number or amount after the increase.
• Calculate the difference by subtracting the original amount from the new amount.
• Finally, divide this difference by the original number, and multiply the result by 100 to get the percentage. This gives you the percentage increase.

For example, the exercise shows a change from $289 to $762. The percent increase is found by finding the difference, dividing by the original, and converting to a percentage, resulting in a 163.7% increase.

Prealgebra and Percentages

Prealgebra serves as the foundation for understanding more complex mathematical concepts. When dealing with percent increases, prealgebra skills come in handy. It involves basic arithmetic skills like addition, subtraction, multiplication, and division, which are crucial when calculating percentage changes. Starting with simple computations, you quickly learn to use formulas to find answers. For example:

• You identify key numbers (original and new values).
• You perform basic subtraction to find differences.
• Finally, you manipulate these numbers into fractions.

All of these steps are basic prealgebra skills that help you tackle percent-related problems confidently and efficiently.

Percent Calculations Simplified

Percent calculations are everywhere, from shopping discounts to finance interest rates. Understanding how to calculate percentages allows you to handle real-world problems with ease and confidence. When calculating percentages, follow these steps to simplify the process:

• Determine the base number (original value).
• Find out the amount of change, either an increase or a decrease.
• Divide the change amount by the base number to get a fraction.
• Convert the fraction to a percentage by multiplying by 100.

Practicing these calculations reinforces your understanding and improves your mathematical fluency. In our example, it shows you how a change from 289 to 762 gives a 163.7% increase, highlighting a significant rise using straightforward calculations.