The enrollment at School R has been increasing by 20 students per year

Question

The enrollment at High School R has been increasing by 20 students per year. Currently High School R has 200 students attending. High School T currently has 400 students, but its enrollment is decreasing in size by an average of 30 students per year. If the 2 schools continue their current enrollment trends over the next few years, how many years will it take the schools to have the same enrollment?

Answer 1

x=# of years

200+20x=400-30x

20x+30x=400-200

50x=200

x=4 years

 

Answer 2

For high school R, the student population at year t is:

 

R(t) = 200 + 20t

 

For high school T, it's:

 

T(t) = 400 - 30t

 

When they have the same enrollment:

 

R(t) = T(t)

200 + 20t = 400 - 30t

 

Solve for t.