Question

At a company, 20% of the employees are part-time employees. There are 33 more full-time employees than part-time employees. What is the total number of employees at this company?

Answer 1

To determine the total number of employees at the company, we can set up a system of equations using x as the number of part-time employees and x + 33 as the number of full-time employees. Solving the system of equations, we find that there are 33 part-time employees and 66 full-time employees, making the total number of employees at the company 99.

Step-by-step explanation:

To solve this problem, we can set up a system of equations. Let x represent the number of part-time employees. Since 20% of the employees are part-time, we know that 0.2 times the total number of employees equals x: 0.2 * (x + (x + 33)) = x.

We also know that there are 33 more full-time employees than part-time employees, so the number of full-time employees is x + 33.

Using these equations, we can solve for x and determine the total number of employees at the company. Let's solve the system of equations:

1. 0.2 * (x + (x + 33)) = x
2. x + 33 = x + (x + 33)

Simplifying the equations:

1. 0.2x + 0.2(x + 33) = x
2. x + 33 = 2x + 33

Combining like terms:

1. 0.2x + 0.2x + 6.6 = x
2. x + 33 = 2x + 33

Combining like terms:

1. 0.4x + 6.6 = x
2. x + 33 = 2x + 33

Subtracting x from both sides:

1. 0.6x = 6.6
2. x = 33

Plugging x back into the equation for the number of full-time employees:

1. x + 33 = 33 + 33
2. x + 33 = 66

Therefore, the number of part-time employees (x) is 33, and the number of full-time employees is 66. The total number of employees at this company is the sum of the part-time and full-time employees, which is 33 + 66 = 99.

Answer 2

The total number of employees at the company is 55.

Step-by-step explanation:

Let's assume the total number of employees at the company is x.

According to the information given, 20% of the employees are part-time employees.

This means that the number of part-time employees is 0.2x.

There are 33 more full-time employees than part-time employees, so the number of full-time employees is 0.2x + 33.

The total number of employees can be found by adding the number of part-time and full-time employees:

x = 0.2x + 0.2x + 33

Combining like terms, we have:

x = 0.4x + 33

Subtracting 0.4x from both sides, we get:

0.6x = 33

Dividing both sides by 0.6, we find:

x = 55

Therefore, the total number of employees at this company is 55.