Question

In 2005, there were 14,700 students at college A, with a projected enrollment increase of 1200 students per year. In the same year, there were 33,400 students at college B, with a projected enrollment decline of 500 students per.

According to these projections, when will the colleges have the same enrollment? What will be the enrollment at that time?
In what year will the two colleges have the same enrollment?"

1.2022, 48,200 students
2.2010, 22,200 students
3.2015, 26,400 students
4.2018, 30,600 students

Answer 1

4.2018, 30,600 students because The colleges will have the same enrollment of 30,600 students in 2018 because, based on the given projections, it takes 11 years from 2005 for college A's increasing enrollment to match and offset college B's declining enrollment.

Step-by-step explanation:

In 2018, both college A and college B will have the same enrollment, reaching 30,600 students. This can be calculated by setting up and solving an equation based on the given information.

Let's denote the number of years from 2005 as (t). For college A, the enrollment can be represented by the equation (14,700 + 1,200t), where 1,200 is the projected increase per year. For college B, the enrollment can be represented by the equation (33,400 - 500t), where 500 is the projected decline per year.

Setting these two equations equal to each other gives us the equation:

[14,700 + 1,200t = 33,400 - 500t.]

Solving for (t), we find:

`\[1,700t = 18,700,\]\[t = (18,700)/(1,700) \approx 11.\]`

So, in 11 years from 2005, which is 2016, the enrollments will be equal. Plugging (t = 11) into either equation, we find the enrollment to be
`(14,700 + 1,200 * 11 = 30,600\)` students.

Therefore, the correct option is 4, in 2018, both colleges will have the same enrollment of 30,600 students.