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.

Question

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.

Answer 1

Let's start by writing the equations for the number of students in each high school after t years:

For High School A:
A(t) = 900 + 50t

For High School B:
B(t) = 1000 + 40t

To find the point in time when High School A will have more students than High School B, we need to set the two equations equal to each other and solve for t:

900 + 50t = 1000 + 40t
10t = 100
t = 10

Therefore, after 10 years, High School A will have more students than High School B.