10. 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?

Let \( x \) be the number of part-time employees. According to the problem, \( 0.2 \) (or \( 20\% \)) of the total employees equals \( x \). Therefore, the number of full-time employees is \( x + 33 \). The total number of employees can be represented as \( x + (x + 33) = 2x + 33 \). Since \( 20\% \) of the total employees is equal to the part-time employees, we have the equation: \[ 0.2(2x + 33) = x \] Now, solving for \( x \): \[ 0.2 \cdot 2x + 0.2 \cdot 33 = x \] \[ 0.4x + 6.6 = x \] \[ 6.6 = x - 0.4x \] \[ 6.6 = 0.6x \] \[ x = \frac{6.6}{0.6} = 11 \] So, there are 11 part-time employees. The number of full-time employees is \( 11 + 33 = 44 \). Thus, the total number of employees is: \[ 11 + 44 = 55 \] The total number of employees at the company is \( \boxed{55} \). In a workplace setting, understanding employee classifications is essential for planning and budgeting. Knowing the ratio of part-time to full-time employees helps management allocate resources effectively, ensuring that project demands are met without overloading staff. Interestingly, the concept of full-time vs. part-time employment has evolved, particularly as companies adapt to more flexible work arrangements. This has led to a rise in gig work and contractual employment, reshaping traditional definitions in modern workforce discussions.