Problem 22 - Prealgebra

Question

Salary Plus Bonus The manager for a computer store is paid a weekly salary of $$ 650\( plus a bonus amounting to \)1.5 \%\( of the net earnings of the store each week. Find her total salary for the week when earnings for the store are $$ 26,875.56 .\) Round your answer to the nearest cent.

Step-by-Step Solution

Answer

The manager's total salary for the week is $1053.13.

Step 1: Calculate Bonus Amount

First, calculate the bonus amount based on the net earnings of the store. The bonus is 1.5% of the weekly earnings. Use the formula for percentage: \( \text{Bonus} = \left(\frac{1.5}{100}\right) \times \text{Net Earnings} \). Substitute the net earnings value. \( \text{Bonus} = \left(\frac{1.5}{100}\right) \times 26875.56 \). Calculate the multiplication to get \( \text{Bonus} = 403.13 \).

Step 2: Calculate Total Salary

Next, add the weekly salary to the calculated bonus to find the manager's total salary for the week. Use the formula \( \text{Total Salary} = \text{Weekly Salary} + \text{Bonus} \). Substitute the known values: \( \text{Total Salary} = 650 + 403.13 \). Add these values to get the total salary \( 1053.13 \).

Key Concepts

Understanding Percentage Calculations

Calculating percentages is a fundamental arithmetic operation. It involves determining a certain proportion or fraction of a whole. In our exercise, the bonus calculation requires us to understand how to apply a percentage to find a specific value. The concept of percentage means "per hundred," so calculating a percentage involves multiplying a number by the fraction or decimal equivalent of the percentage.
For instance, when we are given a store’s net earnings and need to find 1.5% of this amount to calculate the bonus, we convert the percentage into a decimal.

• Convert 1.5% into a decimal by dividing by 100: \( \frac{1.5}{100} = 0.015 \)
• Multiply the net earnings by this decimal: \( 0.015 \times 26875.56 = 403.13 \).

This calculation shows us how much the store manager earns as a bonus, given the percentage of net earnings.

Calculating Bonuses in Salary Contexts

A bonus in a salary context is often a percentage of a specific performance metric, such as sales or net earnings. To calculate this bonus, we first need to determine the percentage of the performance metric that the bonus represents. In our example, the manager receives a bonus that is 1.5% of the store's weekly net earnings.
Understanding how to calculate this is crucial for determining additional earnings beyond the base salary.
Let’s break it down into clear steps:

• Identify the percentage amount: 1.5%.
• Calculate the percentage of the net earnings: \( 0.015 \times 26875.56 = 403.13 \).

This bonus amount is added to the manager's fixed weekly salary to get the total weekly compensation. This formula is significant in various real-world scenarios where earnings are linked to performance metrics like sales or production output.

Basic Arithmetic Operations in Salary Calculations

Understanding basic arithmetic operations like addition and multiplication is essential when computing salaries and bonuses. These operations are used to combine a fixed salary with a fluctuating bonus based on performance, such as net earnings. Here’s how we use these operations in our exercise:

• Multiplication: Used to calculate the bonus amount. By multiplying the net earnings by the decimal form of the percentage, we obtain the bonus.


• Addition: To find the total salary, we add the calculated bonus to the fixed weekly salary: \( 650 + 403.13 = 1053.13 \).

These steps are not only used in this particular problem but are commonly employed in various salary calculation scenarios where employees receive a fixed wage plus a performance-based addition.