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?

Answer: 120

Let X be the total number of employees in the company.

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

$1/ 1 X + 2 X + 1 X + 20 = X$

The denominators are 10, 5, and 3.
The LCD of 10, 5, and 3 is 30.

Rewriting each fraction:

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

Thus, the equation becomes:

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

Rearrange the equation:

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

Multiply both sides by 6:

$X = 120$

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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?