Question

A small town has two local high schools. High School A currently has 750 students and is projected to grow by 45 students each year. High School B currently has 850 students and is projected to grow by 25 students each year. Let A represent the number of students in High School A int 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 after how many years, t, the number of students in both high schools would be the same.​

Answer 1

Equation for high school A: A(t)=750+45t
Equation for high school B: B(t)=850+25t

750+45t=850+25t, solve for t:
45t-25t=850-750
20t=100
t=5

Answer: After 5 years, both high schools will have the same number of students.

Check:
750+45t=750+(45*5)=750+225=975
850+25t=850+(25*5)=850+125=975

Answer 2

Answer: A=750 +75*t

B=900 +25*t

There would be 975 students in each high school in year 3 when they are expected to have the same number of students.

Explanation:

A = B

750 +75*t=900 + 25*t

Solving:

75*t -25*t= 900 - 750

50*t= 150

t=3

This indicates that in year 3 both High Schools are projected to have the same number of students. To get that amount, you simply replace this value in the expressions:

A=750 +75*t= 750 +75*3= 975

B=900 + 25*t=900 + 25*3= 975

There would be 975 students in each high school in year 3 when they are expected to have the same number of students.