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?
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<pre>
Let x be the number of managers to add.


Then the inequality must be held

    {{{(3+x)/(20+3+x)}}} >= 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.


<U>ANSWER</U>.  At least, 2 managers should be hired.
</pre>

Solved.