What percentage of enrolment can be expected to drop?

[Guest]

The Acme Industrial Technical College has fallen on hard times. Last year its enrolment dropped by 20% and this year enrolment dropped another 15% from last year's. Next year the college expects to have 50% of this year's enrolment. What percentage of enrolment can be expected to drop for all 3 years?

[Guest]

Let "E" be the original enrollment.
" Last year its enrolment dropped by 20%" so last year enrollment was .8E. "This year enrolment dropped another 15% from last year's." So this year enrollment is .85(.8E)= 0.68E. "Next year the college expects to have 50% of this year's enrolment." So next year the enrollment is expected to be .5(.68E)= .34E. 100- 34= 66%. Enrollment has dropped 66% over the three years.