Can you solve this problem without using algebra?

Hyere is the problem:
A place sells two different types of ticket, one for $17.50 and one for $20.50. It sells 24 tickets and brings in $459.00. How many of each type of ticket does it sell?

I am sure most of you know how to solve this algebraically. You get two equations: x+y=24 and 17.5x + 20.5y = 459. Then use the mechanics of algebra to magically find x and y.

There is a fun way of solving the problem without algebra. What follows is a hint, which you may think of as a spoiler alert.

Hint:
Start with all 24 tickets costing $17.50. (You can start with any combination of the 24 tickets, and apply similar logic.) 24 tickets at $17.50 will be less than $59.00. Determine how much less to get the additional revenue required. To bring in more money, substitute higher priced tickets for the lower priced ones. How much extra per ticket does a substitution bring in? Divide that number into the additional revenue required to get the number of higher priced tickets sold. Then subtract that number from 24 to get the number of lower priced tickets sold.