Math Word Problem

Question

Suppose the average merch sales at a show is in proportion to how many people purchased tickets. One night a band sells 180 tickets, and at the show it sells $780 of merch. One week later, the band learns that 600 people have purchased tickets for its upcoming show. How many dollars of merch can it expect to sell at its upcoming show?

Answer 1

The problem tells you merch sales and ticket sales are proportional. So, let x = expected merch sales, then set up a proportion and cross-multiply to solve:

 

(night one tickets) / (night one merch) = (night two tickets) / (night two merch)

180/780 = 600/x

180x = 468000

x = 2600

 

The band can expect to sell $2,600 in merch.