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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tonys538's profile pic

tonys538 | Student, Undergraduate | (Level 1) Valedictorian

Posted on

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.

llltkl's profile pic

llltkl | College Teacher | (Level 3) Valedictorian

Posted on

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.

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