Problem 8 - Prealgebra

Question

Salary Increase A person earning \(\$ 3,500\) a month gets a raise of \(\$ 350\) per month. What is the percent increase in salary? \(A\) student reader is making \(\$ 6.50\) per hour and gets a \(\$ 0.70\) raise. What is the percent increase? (Round to the nearest tenth of a percent.)

Step-by-Step Solution

Answer

The percent increase for the monthly salary is 10%, and for the hourly wage is 10.8%.

Step 1: Calculate the Salary Increase

For both parts of the exercise, we need to identify the increase amounts. The salary increase for the first person is \\(350 and for the student is \\)0.70.

Step 2: Find Original Salaries

The original monthly salary for the first person is \\(3,500, and the original hourly wage for the student is \\)6.50.

Step 3: Calculate Percent Increase for Monthly Salary

Use the formula for percent increase: \(\text{Percent Increase} = \left(\frac{\text{Increase Amount}}{\text{Original Amount}}\right) \times 100\). For the monthly salary: \(\frac{350}{3500} \times 100 = 10\%\).

Step 4: Calculate Percent Increase for Hourly Wage

Similarly, for the student: \(\frac{0.70}{6.50} \times 100\approx 10.8\%\).

Step 5: Round the Percent

The percent increase for the student reader is already rounded to the nearest tenth, which is \(10.8\%\).

Key Concepts

Percent Increase Formula

Understanding how to calculate the percent increase is essential for various scenarios. This formula helps us to measure how much something has grown as a percentage of its initial value. The percent increase formula is \[\text{Percent Increase} = \left(\frac{\text{Increase Amount}}{\text{Original Amount}}\right) \times 100\] To use this formula:

• Identify the original amount, which is the starting value before any increase.
• Determine the increase amount, which is the difference between the new value and the original value.
• Divide the increase amount by the original amount to get a decimal.
• Multiply the resulting decimal by 100 to convert it to a percentage.

The formula is effective for a variety of real-world applications, whether for salary increases, price changes, or population growth.

Salary Calculation

In the context of salary calculation, understanding how to determine a percent increase can be important for both employers and employees. Let's break it down using the monthly and hourly scenarios from the exercise. For a monthly salary increase, consider someone who earns \(3,500 each month. If they receive a raise of \)350, it's essential to calculate how much more they are earning as a percentage of their previous salary. The formula given above is applied like this: \[\text{Percent Increase (Monthly)} = \left(\frac{350}{3500}\right) \times 100 = 10\%\] Similarly, an hourly wage scenario where a student earns \(6.50 per hour and receives a \)0.70 raise: \[\text{Percent Increase (Hourly)} = \left(\frac{0.70}{6.50}\right) \times 100 \approx 10.8\%\] Understanding these calculations ensures clarity in how pay raises affect take-home income, and can guide negotiations during a job offer or performance review.

Basic Arithmetic

Basic arithmetic is the foundation of these calculations. Let's explore the simple mathematical concepts you'll need to understand the percent increase formula and salary calculations. At the core of these operations are addition, subtraction, multiplication, and division. To calculate the increase amount: - **Subtraction** is used: The new (higher) number minus the original number gives the increase. - **Division** follows: Divide the increase by the original amount to get a proportion. - **Multiplication** finally: Multiply this proportion by 100 to translate it into a percentage. Applying these steps, you can solve percent increase problems effectively: For example:

• Subtract the old salary from the new salary to get an increase.
• Divide the increase by the original salary to find the proportion.
• Multiply by 100 to express it as a percentage increase.

No matter how complex the numbers may seem, they boil down to these basic arithmetic operations. Mastering these basics can help you tackle more complex financial calculations in everyday scenarios.