Question

A small town has two local high schools. High School A currently has 1000 students and is projected to grow by 35 students each year. High School B currently has 700 students and is projected to grow by 55 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 after how many years, t, commat, the number of students in both high schools would be the same.

Answer 1

Step-by-step explanation:

Equation for High School A (A_t):

A_t = 1000 + 35t

Equation for High School B (B_t):

B_t = 700 + 55t

To find the number of years (t) after which the number of students in both high schools would be the same, set A_t equal to B_t:

1000 + 35t = 700 + 55t

Solving for t:

300 = 20t

t = 15

After 15 years, the number of students in both High School A and High School B would be the same.

Answer 2

The number of students in High School A and High School B will be the same after 15 years given the equations AA = 1000 + 35t for School A and BB = 700 + 55t for School B.

Step-by-step explanation:

To determine after how many years t the number of students in both high schools would be the same, we can set up two linear equations representing the growth of each school.

The equation for High School A (AA) is AA = 1000 + 35t, indicating that the school starts with 1000 students and grows by 35 students per year.

The equation for High School B (BB) is BB = 700 + 55t, representing the initial 700 students with an annual growth of 55 students.

To find when the number of students is the same (AA = BB), we set the two equations equal to each other:

1000 + 35t = 700 + 55t

To solve for t, we rearrange the terms:

35t - 55t = 700 - 1000

-20t = -300

t = 300 / 20

t = 15

It will take 15 years for the number of students in both High School A and High School B to be the same.