Answer :
Equation for High School 'A'. Number of students after 't' years:
T₁ = 85t + 650
Equation for High School 'B'. Number of students after 't' years:
T₂ = 60t + 800
After 6 years the number of students in both high schools would be same.
How to write Equation of Line?
The equation of a line is typically written as y = mx + b
where,
m is the slope.
b is the y-intercept.
using equation of line we can find the equation for both high school.
we can also write the equation of line:
T = [tex]\frac{dx}{dt}[/tex] x t + C.
where,
T → total number of students after 't' years
[tex]\frac{dx}{dt}[/tex] → the rate at which students are increasing per year.
C → Initial number of students.
We have given that High school 'A' initially has 650 students and grow by 85 students each year.
so, we can say that, Number of students after 't' years:
T₁ = 85t + 650
here, T → Total number of students after 't' years.
650 → initial numbers of students.
85 → the [tex]\frac{dx}{dt}[/tex] rate at which students are increasing per year.
We have given that High school 'B' initially has 800 students and grow by 60 students each year.
so, we can say that, Number of students after 't' years:
T₂ = 60t + 800
here, T → Total number of students after 't' years.
800 → initial numbers of students.
60 → the [tex]\frac{dx}{dt}[/tex] rate at which students are increasing per year.
For the number of students to be equal we will equate the equation T₁ and T₂ equal.
T₁ = T₂
85t + 650 = 60t + 800
25t = 150
t = 6 years
Hence,
Equation for High School 'A'. Number of students after 't' years:
T₁ = 85t + 650
Equation for High School 'B'. Number of students after 't' years:
T₂ = 60t + 800
After 6 years the number of students in both high schools would be same.
Learn more about "Equation Formation and Variable" from here: https://brainly.com/question/11897796
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