Question

in 2020, there were 15,900 students at college a, with a projected enrollment increase of 750 students per year. in the same year, there were 33,400 students at college b, with a projected enrollment decline of 1000 students per year. according to these projections, when will the colleges have the same enrollment? what will be the enrollment in each college at that time? in the year , the enrollment at both colleges will be the same. the total enrollment at each college will be students.

Explanation:

Step1: Set up an equation for the number of years passed

Let $x$ be the number of years after 2020 when the enrollments are the same.
The enrollment of college A after $x$ years is $15900 + 750x$.
The enrollment of college B after $x$ years is $33400-1000x$.
We set up the equation $15900 + 750x=33400 - 1000x$.

Step2: Solve for $x$

First, add $1000x$ to both sides of the equation:
$15900 + 750x+1000x=33400 - 1000x+1000x$.
$15900 + 1750x=33400$.
Then subtract 15900 from both sides:
$1750x=33400 - 15900$.
$1750x=17500$.
Divide both sides by 1750:
$x=\frac{17500}{1750}=10$.

Step3: Find the enrollment in each college at that time

Substitute $x = 10$ into the equation for college A's enrollment (we could also use college B's equation).
$y=15900+750\times10$.
$y=15900 + 7500$.
$y = 23400$.

Answer:

23400