How many of each kind of ticket would be sold?

Question

Tickets for a show cost $18, $21 or, for VIP, $40. If 10 times as many $18 tickets were sold as VIP tickets, and the number of $18 tickets sold was 57 more than the sum of the number of $21 and $40 tickets, sales of all three kinds would total $51,973.

Answer 1

$18 tickets are being compared to vip tickets.

So let x = the number of vip tickets sold.

Then 10x = the number of $18 tickets sold.

Let y = the number of $21 tickets sold.

the number of $18 tickets sold was 57 more than the sum of the number of $21 and $40 tickets

The above translates to 10x = x+y +57

You can solve this for y. y = 9x - 57.

The total cost will then be ????? = $51,973