Answered

IDNLearn.com: Your go-to resource for finding precise and accurate answers. Discover reliable answers to your questions with our extensive database of expert knowledge.

In 2020 , there were 12,900 students at college A, with a projected enrollment increase of 500 students per year. In the same year, there were 24,150 students at college B, with a projected enrollment decline of 750 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.

Sagot :

Sqdancefanidn

Answer:

  • 2029
  • 17400 students

Step-by-step explanation:

If enrollment at A in 2020 is 12,900, increasing at 500 per year, and enrollment at B is 24,150, decreasing at 750 per year, you want to know the year the enrollments are the same, and what that enrollment is.

Setup

We can write equations for the enrollment as a function of year for each college:

  A = 12900 +500(x -2020)
  B = 24150 -750(x -2020)

where x is the year, and A, B are the enrollments.

Solution

We have A = B when ...

  A = B

  12900 +500(x -2020) = 24150 -750(x -2020)

  1250(x -2020) = 11250 . . . . . . . . add 750(x -2020) -12900

  x -2020 = 9 . . . . . . . . . . . . . . . divide by 1250

  x = 2029

  A = 12900 +500(9) = 17400

In the year 2029, enrollment at both colleges will be 17,400 students.

Thank you for contributing to our discussion. Don't forget to check back for new answers. Keep asking, answering, and sharing useful information. IDNLearn.com is committed to providing the best answers. Thank you for visiting, and see you next time for more solutions.