Question

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 $a$ represent the number of students in high school a in $t$ 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
$a =$ $b =$
answer:

Explanation:

Step1: Define equation for School A

$A = 1000 + 35t$

Step2: Define equation for School B

$B = 700 + 55t$

Step3: Set equations equal (same enrollment)

$1000 + 35t = 700 + 55t$

Step4: Rearrange to isolate t terms

$1000 - 700 = 55t - 35t$

Step5: Simplify both sides

$300 = 20t$

Step6: Solve for t

$t = \frac{300}{20}$

Answer:

$A = 1000 + 35t$
$B = 700 + 55t$
$t = 15$