1490.21 – Prom Bands

It is time to hire the band for the prom! The Walldogs will play for $2500 plus 50 percent of the money taken in from ticket sales. The Three Hundos will play for a flat fee of $5500. Three hundred couples are expected to attend.

What is the most you can charge per couple so that The Walldogs are cheaper than The Three Hundos?

Solution

Let us say that the charge is dd dollars per ticket per couple. The income will be $300dd. The Walldogs would get

$2500+$300d⋅0.50=$2500+$150d.\$2500 + \$300 d \cdot 0.50 = \$2500 + \$150 d.

The Three Hundos would get $5500. We want The Walldogs to be cheaper, so

2500+150d<5500,150d<3000,d<20. \begin{aligned} 2500 + 150d &<& 5500, \\ 150d &<& 3000, \\ d &<& 20. \end{aligned}

Therefore charge $19.99 per couple. (Or not)