In 2005 there were 14000 students at college A, with a projected enrollment increase of 750 students per year. In the same year there were 35000 students at college B with a projected enrollment decline of 1000 students per year. According to these projectors when will the colleges have the same enrollment? What will be the enrollment in each college at that time

Question

Mathematics

Rigoberto

11 May, 02:19

In 2005 there were 14000 students at college A, with a projected enrollment increase of 750 students per year. In the same year there were 35000 students at college B with a projected enrollment decline of 1000 students per year. According to these projectors when will the colleges have the same enrollment? What will be the enrollment in each college at that time

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Answers (1)

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Hazel Swanson · Answer 1

Answer: in 12 years (2017)

23,000 students enrolled

Step-by-step explanation:

Let x represent the number of years since 2005.

Let y represent the number of students enrolled.

College A: y = 14,000 + 750x

College B: y = 35,000 - 1000x

Solve the system using the Substitution Method:

14,000 + 750x = 35,000 - 1000x

+1000x + 1000x

14,000 + 1750x = 35,000

-14,000 - 14,000

1750x = 21,000

x = 12

Input x = 12 into one of the equations to solve for y.

y = 35,000 - 1000x

= 35,000 - 1000 (12)

= 35,000 - 12,000

= 23,000