In 2005, there were 12,300 students at college A, with a projected enrollment increase of 500 students per year. In the same year there were 18,550 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 the enrollment in each college at that time?
Accepted Solution
A:
Answer: 5 years 14,800 students enrolledStep-by-step explanation:Let x represent the number of years andLet y represent the number of students enrolled College A: y = 12,300 + 500xCollege B: y = 18,550 - 750xUse substitution Method to solve:12,300 + 500x = 18,550 - 750x +750x +750x 12,300 + 1250x = 18,550-12,300 -12,300 1250x = 6250 x = 5Input x = 5 into one of the equations to solve for y.y = 12,300 + 500x = 12,300 + 500(5) = 12,300 + 2500 = 14,800