Question

For a certain event, 817 tickets were sold, for a total of $1919. If students paid $2 per ticket and nonstudents paid $3 per ticket, how many student tickets were sold?

Answer 1

532 student tickets were sold

Explanation:

Let x be the no. of student's tickets sold

Let y be the no. of non student's tickets sold

We are given that 817 tickets were sold in total

So,
`x+y = 817` --1

Cost of 1 student's ticket = $2

So, Cost of x student's ticket = 2x

Cost of 1 non - student's ticket = $3

Cost of y non - student's ticket = 3y

We are given that 817 tickets were sold, for a total of $1919

So,
`2x+3y = 1919` ---2

Solving 1 and 2

Substitute the value of y from 1 in 2

`2x+3(817-x) = 1919`

`2x+2451-3x = 1919`

`2451-1919=x`

`532=x`

Substitute the value of x in 1

`532+y = 817`

`y = 817-532`

`y = 285`

Hence 532 student tickets were sold