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?

Tags:
Solution

Let us say that the charge is dd dollars per ticket per couple. The income will be d×$300d \times \$300. 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)