Problem 90 - Prealgebra

Question

Compensation Each of three employees earned an annual salary of \(545,000\) before Employee A was given a \(3 \%\) raise, Employee B was given a \(6 \%\) raise, and Employee C was given a \(4.5 \%\) raise. Which of the three employees now has the highest annual salary? Explain how you arrived at your answer.

Step-by-Step Solution

Answer

Employee B now has the highest annual salary at 577,700.

Step 1: Determine Employee A's New Salary

Employee A's salary is initially 545,000. They receive a 3% raise. To find the amount of the raise, calculate 3% of 545,000: \[ \text{Raise for A} = 0.03 \times 545,000 \].This equals 16,350. So, the new salary for Employee A is:\[ \text{New salary for A} = 545,000 + 16,350 = 561,350 \].

Step 2: Calculate Employee B's New Salary

Employee B also starts with a salary of 545,000. They receive a 6% raise. Compute 6% of 545,000 to know the raise amount:\[ \text{Raise for B} = 0.06 \times 545,000 \].This equals 32,700.Therefore, Employee B's new salary is:\[ \text{New salary for B} = 545,000 + 32,700 = 577,700 \].

Step 3: Find Employee C's New Salary

Employee C's initial salary is the same, 545,000. They receive a 4.5% raise. Calculate 4.5% of 545,000 for the raise:\[ \text{Raise for C} = 0.045 \times 545,000 \].This equals 24,525.Thus, Employee C's new salary is:\[ \text{New salary for C} = 545,000 + 24,525 = 569,525 \].

Step 4: Compare the New Salaries

Now, we compare the employees' new salaries: - Employee A: 561,350 - Employee B: 577,700 - Employee C: 569,525 From the calculations, Employee B has the highest new salary at 577,700.

Key Concepts

Salary Increase

When an employee receives a salary increase, it means their annual pay has been adjusted according to a specified percentage. To calculate the new salary after an increase, multiply the current salary by the percentage increase to find the raise amount.
Add this raise to the original salary to determine the new total. For example, a 3% raise on a salary of 545,000 results in a new salary of:

• Calculate 3% of 545,000: \( 0.03 \times 545,000 \)
• This results in an additional 16,350.
• Add that to the original salary: \( 545,000 + 16,350 = 561,350 \).

This method ensures that you accurately compute any salary adjustments.

Employee Compensation

Employee compensation encompasses more than just salary. It includes all forms of pay or benefits provided in return for the work performed. However, understanding how salary increases affect overall compensation is crucial.
In our example, all employees started with the same base salary of 545,000. Different raise percentages mean different final salaries:

• Employee A received a 3% increase.
• Employee B's raise was 6%.
• Employee C enjoyed a 4.5% increase.

These varying percentages directly impact their compensation, illustrating how percentage calculations are used to determine pay adjustments promoted by raises.

Comparing Values

To determine which employee has the highest salary after the raise, it’s essential to compare the calculated values.
A crucial skill in decision-making, comparing values involves evaluating the new salaries side by side:

• Employee A: 561,350
• Employee B: 577,700
• Employee C: 569,525

The comparison distinctly shows that Employee B now earns the most, as 577,700 is the highest among the three. This comparison helps in understanding the impact of different raise percentages on final outcomes, emphasizing the importance of analysis in employee compensation decisions.