word problem

Question

A 20,000 seat amphitheater will sell tickets at $50 and $75 for a Green Day concert. Let x and y be the number of tickets that will sell for $50 and $75, respectively. Assume the show will sell out.

A) Let R=f(x) be the total revenue (In dollars) from selling the $50 and $75 tickets. Find an equation of f.

Answer 1

x + y = 20,000 for the simplest relationship for the tickets sold.

 

The revenue is R = 50x + 75y.

 

Writing the revenue equation only in x, we get R = f(x) = 50x + 75(20,000 - x) = 1,500,000 - 25x.