Let n represent students and m represent non-students.
The total number who attended was 1100. Meaning if we add both the students and non students, we should be 1100.
[tex]m+n=1100---eqn(1)[/tex]
The paid a gate fee of $2 while non students paid $3 and the total was $2800
[tex]3m+2n=2800---eqn(2)[/tex]
We now solve the two equations simultaneously.
Let us make m the subject in equation (1) to get
[tex]m=1100-n---eqn(3)[/tex]
Now, let us put (3) in equation (2) to obtain,
[tex]3(1100-n)+2n=2800[/tex]
We expand solve for m.
[tex]3300-3n+2n=2800[/tex]
[tex]-3n+2n=2800-3300[/tex]
Simplify to obtain,
[tex]-n=-500[/tex]
Divide through by -1
[tex]n=500[/tex]
Substitute this value into equation (3)
to obtain,
[tex]m=1100-500=600[/tex]
Therefore 600 were sold to non students while 500 were sold to students.
In other word 500 pieces of the $2 and 600 pieces of $3 were sold.
