A small town has two local high schools. High School A currently has 850 students and is projected to grow by 45 students each year. High School B currently has 700 students and is projected to grow by 75 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, commat, and determine which high school is projected to have more students in 8 years.

Question

Answer
Attempt 1 out of 2

A, equalsA=
B, equalsB=

will have
more students than
in 8 years.

Answer 1

Let's begin by writing the equations for the number of students in each high school after \( t \) years.

For High School A:

• Current students = 850
• Growth per year = 45 students

The equation for the number of students in High School A after \( t \) years is: \[ A(t) = 850 + 45t \]

For High School B:

• Current students = 700
• Growth per year = 75 students

The equation for the number of students in High School B after \( t \) years is: \[ B(t) = 700 + 75t \]

Now, we want to find out which high school will have more students in 8 years. We can substitute \( t = 8 \) into both equations.

For High School A: \[ A(8) = 850 + 45(8) = 850 + 360 = 1210 \]

For High School B: \[ B(8) = 700 + 75(8) = 700 + 600 = 1300 \]

Now, comparing the two results:

• High School A will have 1210 students.
• High School B will have 1300 students.

So, in 8 years, High School B will have more students than High School A.

Final answer:

• \( A(t) = 850 + 45t \)
• \( B(t) = 700 + 75t \)
• High School B will have more students than High School A in 8 years.