Question 52910
Age of the Auditorium = unknown = n
Age of the Gym = n-21 [The gym is 21 years newer than the auditorium]
Age of the Gym = (1/4)n [the gym is also one fourth as old as the auditorium]
Gym = Gym
So, n-21=(1/4)n 
n-n-21=(1/4)n-n [Isolate all of the terms to one side of the equation]
21=(3/4)n
0=(3/4)n-21 [Equation of the problem]
.

(3/4)n -21=0 [solve for "n"]
(3/4)n-21+21=0+21
(3/4)n=21
(4/3)(3/4)n=(21)(4/3)
n=28= the age of the auditorium
.
Check by plugging (n=28) back into the original equations
Age of the Gym = n-21 = 28-21=7
Age of the Gym = (1/4)n = (1/4)(28/1)=7
[checks out]