Problem 23 - 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 teacher making \(\$ 43,752\) per year gets a \(6.5 \%\) raise. What is the new salary?

Step-by-Step Solution

Answer

The new salary is $46,595.88.

Step 1: Determine the Raise Amount

To find the raise amount, we need to calculate 6.5% of the original salary of $43,752. Convert the percentage to a decimal by dividing by 100: \[ 6.5\% = \frac{6.5}{100} = 0.065 \] Now, multiply this decimal by the original salary: \[ 0.065 \times 43,752 = 2,843.88 \] This is the amount of the raise in dollars.

Step 2: Calculate the New Salary

Add the raise amount to the original salary to get the new salary. The original salary is \(43,752 and the raise is \)2,843.88, so: \[ \text{New Salary} = 43,752 + 2,843.88 = 46,595.88 \] This is the new salary after the raise.

Key Concepts

Salary Calculation

Understanding how to calculate salary changes is an essential skill, especially when dealing with raises. Let's consider a scenario: a teacher's salary is $43,752 per year and they receive a 6.5% raise. The first step is determining how much more the teacher will earn annually due to this raise. This involves multiplying the current salary by the percentage increase. However, ensure the percentage is converted into decimal form first. Once you have the raise amount, simply add that to the current salary to find out the new annual salary. This step-by-step approach allows you to dissect each part of the calculation, making the process straightforward. Breaking it down prevents errors and makes the math less daunting. Remember:

• Start with the original salary.
• Determine the raise amount by converting the percentage to a decimal and multiplying.
• Add the raise to the original salary to get the new salary.

Percentage to Decimal Conversion

Converting percentages to decimals is a fundamental math skill. This conversion simplifies multiplying percentages with other numbers. The key is to remember that "percent" means "per hundred." Therefore, converting a percentage to a decimal involves dividing the percentage figure by 100. Taking the example of a 6.5% raise, to turn this percentage into a decimal, divide 6.5 by 100. This gives 0.065. This decimal format is what you use in calculations. Without converting, multiplying by the percentage directly would result in incorrect figures. Here’s a quick guide to converting:

• Move the decimal point two places to the left.
• So, 6.5% becomes 0.065.
• This small change makes calculations with percentages easier and accurate.

Using a Calculator

Using a calculator for percentage calculations can save time and reduce errors. The steps involved in the calculation of a salary increase are straightforward when using a calculator. Make sure your calculator is set to standard mode, or reset if it has been used for different functions like scientific calculations. Steps to follow:

• Convert the percentage to a decimal if not already done.
• Input the decimal into the calculator, followed by the multiplication sign (×).
• Insert the original salary amount and calculate to find the raise amount.
• Finally, add the raise amount to the original salary using the calculator for the new total salary.

By relying on a calculator for each step, particularly in converting percentages and performing multiplications and additions, you minimize error chances. This small tool can greatly enhance accuracy and efficiency.