what is the maximum number of additional accountants that should be hired to meet these plans?

Question

15 people are employed, 20% of whom are typists. If management plans to keep a current number of typists, but to increase the number of accounting staff to the point where 12% of the total stuff are typists, what is the maximum number of additional accountants that should be hired to meet these plans?

Answer 1

15 are employed, 20% are typists. That's 15(.2) = 3 typists, 15-3 = 12 are not typists

12% = 3/(15 + x)

= .12 = 3/(15+x) where x = new employees added who are not typists

.12(15 + x) = 3

12(15+x) = 300

180 + 12x = 300

12x = 300-180 = 120

x = 120/12 = 10 more accountants or non-typist employees can be added to the 15 employees, reducing the percentage of typists from 20% to 12%

3/15 = 1/5 = 20%

3/(15+10) = 3/25 = 12/100 = 12%