Let x be the total number of staff in the office.
Thus,
The number of staff on vacation = [tex] \frac{1}{3} x[/tex]
Since, it says that staff out sick are among those not on vacation, we have to subtract the number of staff on vacation from the total number of staff.
The number of staff out sick = [tex] \frac{1}{4} (x - \frac{1}{3}x)[/tex]
Hence,
The number of staff in the office = [tex]x - \frac{1}{3} x - \frac{1}{4} (x- \frac{1}{3} x) = (x - \frac{1}{3} x)(1 - \frac{1}{4} )
= x(1- \frac{1}{3})(1- \frac{1}{4}) = x( \frac{2}{3})( \frac{3}{4}) [/tex] [tex]= \frac{1}{4} x[/tex]
