Question 626893: In 2005, there were 11,500 students at college A, with a projected enrollment increase of 1,200 students per year. In the same year, there were 22,700 students at college B, with a projected enrollment decline of 400 students per year. in what year will the two colleges have the same enrollment? At that time how many students be enrolled in both colleges?
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! In 2005, there were 11,500 students at college A, with a projected enrollment increase of 1,200 students per year. In the same year, there were 22,700 students at college B, with a projected enrollment decline of 400 students per year. in what year will the two colleges have the same enrollment? At that time how many students be enrolled in both colleges?
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We have two straight line equations that take the standard form: y=mx+b, m=slope, b=y-intercept.
For given problem, college A:
y-intercept, b=11500
slope, m=1200 students per year increase
equation: y=1200x+11500 (number of students for given year x)
..
For given problem, college B:
y-intercept, b=22700
slope, m=-400 students per year decrease
equation: y=-400x+22700 (number of students for given year x)
..
When number of students are the same for both colleges:
1200x+11500=-400x+22700
1600x=11200
x=11200/1600
x=7
y=1200x+11500=19900.
..
The two colleges will have the same enrollment in year 2012
Number of students enrolled at both colleges at this time: 19,900
note: It would be instructive to plot both equations on an x-y coordinate system and see that the answer is the point of intersection of these two equations.
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