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?

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​/5X
• Production department:1​/3X
  
• Marketing department: 20 employees (given)

Step 3: Form the Equation

Since the sum of all employees equals the total number $X$, we write:

1/1​0X+2​/5X+1​/3X+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​0X=3./3​0X$$frac{2}{5}X = frac{12}{30}X$$1/3​X=10/30​X

Thus, the equation becomes:

3/3​0X+12​/30X+10​/30X+20=X $$frac{25}{30}X + 20 = X$$

Step 5: Solve for X

Rearrange the equation:

20=X−25​/30X
20=5/30​X $$20 = frac{1}{6}X$$

Multiply both sides by 6:

$$X = 120$$

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