SOLUTION: An office has 3 managers and 20 employees. If admins want to change the office setup to have at least 20% of the work force (managers and employees) consist of managers, how ma

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: An office has 3 managers and 20 employees. If admins want to change the office setup to have at least 20% of the work force (managers and employees) consist of managers, how ma      Log On


   

Question 1195908: An office has 3 managers and 20 employees.
If admins want to change the office setup to have at least 20% of the work force (managers and employees) consist of managers,
how many managers need to be hired at a minimum?
Answer by ikleyn(52835) About Me  (Show Source):
You can put this solution on YOUR website!
.
An office has 3 managers and 20 employees.
If admins want to change the office setup to have at least 20% of the work force
(managers and employees) consist of managers,
how many managers need to be hired at a minimum?
~~~~~~~~~~~~~~~ 

Let x be the number of managers to add.


Then the inequality must be held

    %283%2Bx%29%2F%2820%2B3%2Bx%29 >= 0.2.


Multiply both sides by 23+x and simplify

    3 + x >= 0.2*(23+x)

    3 + x >= 4.6 + 0.2x

    x - 0.2x >= 4.6 - 3

      0.8x   >=    1.6

         x   >=    1.6/0.8 = 2.


ANSWER.  At least, 2 managers should be hired.

Solved.