Question

A small town has two local high schools. High School A currently has 850 students and is projected to grow by 75 students each year. High School B currently has 1000 students and is projected to grow by 65 students each year. Let AA represent the number of students in High School A in tt years, and let BB represent the number of students in High School B after tt years. Write an equation for each situation, in terms of t,t, and determine which high school is projected to have more students in 11 years.

Answer 1

For High School A, let denote the number of students after years. Define analogously.

Then and .

After 6 years the number of students in both high schools would be the same.

Explanation:

For High School A, let denote the number of students after years. Define analogously.

Since we start out at 850 students at High School A and it is growing by 35 students every year, we must have that .

Since we start out at 700 students at High School B and it is growing by 60 students every year, we must have that .

Setting the two equations equal to each other, we see that

So after 6 years the number of students in both high schools would be the same.