SOLUTION: There is a report in the meeting room. If 4 people sit per bench 1 extra bench is needed. If 6 people sit per bench 4 benches are left vacant. How many people are attending the rep

Let n be the number of people and "b" be the number of benches.


Then the condition gives you these two equations:

 = b + 1,    (1)

 = b - 4.    (2)


It is literal translation of the condition to equations.


You can rewrite eqs (1) and (2) in the form

n = 4b +  4,         (1')
n = 6b - 24.         (2')


It implies 4b + 4 = 6b - 24  ====>  24 + 4 = 6b - 2b   ====>  2b = 28  ====>  b= 14.


Then n = 4b + 4 = 4*14 + 4 = 60.


Answer.  60 people and 14 benches.


Check.   60/4 = 15 = 14+1  <====>  1 extra bench.

         60/6 = 10  <====>  4 benches are vacant.     ! Correct !