It is time to hire the band for the prom. Band A will play for $2500 plus 50% of the money taken in from ticket sales. Band B will play for the flat fee of $5500. You expect 300 couples to attend. What is the most you can charge per couple so that Band A is cheaper than Band B?
Charge $d per ticket per couple. The income will be 300d.
Band A gets $2500 + 300d · 50% = 2500 + 150d.
Band B gets $5500.
We want Band A to be cheaper:
2500 + 150d < 5500
150d < 3000
d < 20
So, charge $19.99 per couple.