A small town has two local high schools. High School A currently has 900 students and is projected to grow by 50 students each year. High School B currently has 1000 students and is projected to grow by 40 students each year. Let A represent the number of students in High School A in t years, and let B represent the number of students in High School B after t years. Write an equation for each situation, in terms of t, and determine the interval of years, t, for which High School A will have more students than High School B.
The equation for the number of students in High School A after t years is A = 900 + 50t.
The equation for the number of students in High School B after t years is B = 1000 + 40t.
To find the interval of years for which High School A will have more students than High School B, we need to solve the inequality A > B.
Substitute the equations for A and B into the inequality:
900 + 50t > 1000 + 40t
Simplify the inequality:
10t > 100
Divide by 10:
t > 10
Therefore, High School A will have more students than High School B after 10 years.