1. At a company, 1/10 of the employees work in the accounting department, 2/5 work in sales, 1/3 work in production, and the remaining 20 work in marketing. How many employees does the company have?
- A. 300
- B. 120
- C. 40
- D. 150
Check answer and explanation
Answer: 120
Explanation Step 1: Define Variables Let X be the total number of employees in the company. Step 2: Express the Given Information in Terms of X Accounting department: 1/10 X Sales department: 2 /5 X Production department: 1 /3 X Marketing department: 20 employees (given) Step 3: Form the Equation Since the sum of all employees equals the total number X X , we write: 1/ 1 0 X + 2 /5 X + 1 /3 X + 20 = X Step 4: Find the Least Common Denominator (LCD) The denominators are 10, 5, and 3. The LCD of 10, 5, and 3 is 30. Rewriting each fraction: 1/ 1 0 X = 3./ 3 0 X frac{2}{5}X = frac{12}{30}X 2 /5 X = 12 /30 X 1/3 X = 10/30 X Thus, the equation becomes: 3/ 3 0 X + 12 /30 X + 10 /30 X + 20 = X frac{25}{30}X + 20 = X 25 /30 X + 20 = X Step 5: Solve for X Rearrange the equation: 20 = X − 25 /30 X 20 =5/ 30 X 20 = frac{1}{6}X 20 = 1/6 X Multiply both sides by 6: X = 120 X = 120