Helen K.

asked • 01/05/18

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

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?

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Philip P. answered • 01/05/18

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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.
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Chandler R.

What method would you use?
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11/17/20

Philip P.

The enrollment equations for schools R and T are linear because they change by the same amount each year. When the schools have the same enrollment, the enrollments are equal. You can find the value by setting the two equations equal and solving for t (which is what both I and Arthur did) or you can graph the two lines and see where they cross. I chose the algebraic method (set the equations equal and solve for t).
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11/17/20

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