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.