Word problem below

Question

A league fee is $825 divided equally by members.  if there were 4 more members, each member would pay $20 less.  Know answer is 11.  Need to understand how to get equation to solve.

Answer 1

If number of members is N, then each member pays 825/N dollars.
For N+4 members they would each pay $20 less, so each member would pay ($825/N)-$20=$825/(N+4).
We needto solve this equation. Start by multiplying through by N(N+4):
825(N+4)-20N(N+4)=825N. 825N+3300-20N^2-80N=825N.
20N^2+80N-3300=0. This simplifies: N^2+4N-165=0 and factorises: (N-11)(N+15) =0. The positive root is N=11, which confirms your statement.