Question

Solve. CAN'T COPY THE TABLE Lou’s current annual salary is $23,800. If he receives a 6.5% raise, what is his new salary?

Short answer

Answer: Lou's new annual salary is $25,347.

Step-by-step solution

Convert the percentage raise to decimal form

To convert 6.5% to decimal form, divide it by 100: 6.5 / 100 = 0.065.

Calculate the amount of the raise

To determine the amount of the raise, multiply Lou's current annual salary (\(23,800) by the decimal form of the percentage raise (0.065): \)23,800 * 0.065 = $1,547.

Calculate Lou's new salary

To calculate Lou's new salary, add the amount of the raise (\(1,547) to his current annual salary (\)23,800): \(23,800 + \)1,547 = $25,347. Lou's new annual salary after the 6.5% raise is $25,347.

Key concepts

Converting Percentages to Decimals

Understanding how to convert percentages to decimals is a fundamental skill in prealgebra that can be applied in various contexts, such as computing salary increases. For example, to calculate a raise, one must first convert the percentage of increase to decimal form. To do so, you simply divide the percentage by 100. For instance, a 6.5% raise is converted to decimal by dividing 6.5 by 100, which equals 0.065.

Here's why this step is crucial: Percent means 'per hundred,' so when you are given a percentage, it represents that many hundredths. Therefore, you divide by 100 to determine how many units of one you have. If 6.5% were 6.5 per one, it would not be a percentage, so converting ensures that you're working with the right values for calculations.

Calculating Percentage Increase

Calculating percentage increase allows individuals to determine how much a certain value has gone up. To calculate the increase, you multiply the original amount by the percentage in decimal form. In the context of a salary raise, after converting the raise percentage to a decimal, you multiply the original salary by this decimal. This gives the actual increase in dollars.

For example, with Lou's raise of 6.5%, once we have the decimal form (0.065), we multiply Lou's current salary of \(23,800 by 0.065 to get \)1,547, which is the raise amount. This basic operation is vital in financial planning and budgeting as it translates percentage changes into tangible dollar amounts.

Basic Algebraic Operations

Basic algebraic operations include addition, subtraction, multiplication, and division. These operations are the backbone of handling percentage problems. In our exercise, we first multiplied the salary by the decimal to find the raise amount (multiplication), and then we added that amount to the original salary to find the new salary (addition).

It is important to perform these operations in the correct order, which, in this case, is following the order of operations also known as BODMAS/BIDMAS (Brackets, Orders/powers, Division and Multiplication, Addition and Subtraction). Understanding and correctly applying these operations are essential for solving problems not just in prealgebra, but across virtually all areas of mathematics.