# This year the college enrolled 1,784 students. This represents an increase for the last two years. Last year the enrolment went up by 1/5 and this year a further increase of 300 students. How...

This year the college enrolled 1,784 students. This represents an increase for the last two years. Last year the enrolment went up by 1/5 and this year a further increase of 300 students. How many were enrolled two years ago? Round your final answer properly to the nearest whole number.

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The number of students enrolled this year is equal to 1784. The enrollment this year is 300 greater than it was last year. The enrollment last year was 1784 - 300 = 1484. The enrollment last year was 1/5 more than that 2 years ago. The enrollment 2 years ago was `1484/(1+1/5) = 1484/(6/5) = (5*1484)/6` = 1236.6

As the number of students has to be a positive integer, the enrollment two years ago was 1237.

Let no. of students enrolled two years ago be x.

Last year the enrolment went up by 1/5 and this year a further increase of 300 students.

The total number of students this year is 1784.

Therefore, by condition:

`x+x/5+300=1784`

`rArr (6x)/5=1484`

`rArr x=(1484*5)/6=1236.667`

The nearest whole number rounded is `x=1237`

**Therefore, there were 1237 students enrolled two years ago.**