solving word problems-algebra 2

Question

In planning for a school dance, you find that one band will play for $250, plus 50% of the total ticket sales. Another band will play for a flat fee of $550. In order for the first band to produce more profit for the school than the other band, what is the highest price you can charge per ticket, assuming 300 people attend?

Answer 1

Let x = price per ticket. If 300 people attend, total ticket sales will be 300x.

First band cost will be 250 + 0.5(300x). That's a fee of $250 + 50% of total ticket sales.

250 + 0.5(300x) = 550 (compare 1st band with 2nd band's flat fee). Solve for x.

250 + 150x = 550

150x = 300

x = $2/ticket for both band costs to be $550.

Re: profit for the school - a higher price would make the 1st band's costs higher than 2nd band (flat fee). Also, would you still sell 300 tickets at a higher ticket price?