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

Here's a start:
The profit you make from the first band is the total amount of money taken in minus the amount you have to pay the band. Call the ticket price x. Write expressions for:
1. The total amount of money taken in
2. The amount paid to the first band
3. The profit from the first band (expression 1 minus expression 2)

Answer 2

Then do the same for the second band. Then you will have two expressions (in x): the profit you make from the first band and the profit you make from the second band. Use them to construct an inequality, then solve for x.