Question

a total of 1100 people attended a school concert the admission was 2 dollar for student and 3 for non student if the total gate were 2800 dollar how many of each type of ticket were sold?

Answer 1

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.

`m+n=1100---eqn(1)`

The paid a gate fee of $2 while non students paid $3 and the total was $2800

`3m+2n=2800---eqn(2)`

We now solve the two equations simultaneously.

Let us make m the subject in equation (1) to get

`m=1100-n---eqn(3)`

Now, let us put (3) in equation (2) to obtain,

`3(1100-n)+2n=2800`

We expand solve for m.

`3300-3n+2n=2800`

`-3n+2n=2800-3300`

Simplify to obtain,

`-n=-500`

Divide through by -1

`n=500`

Substitute this value into equation (3)

to obtain,

`m=1100-500=600`

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.