mixture problem

Question

A 12,500-seat amphitheater will sell tickets at $44 and $73 for a concert. Let x and y be the number of tickets that will sell for $44 and $73, respectively. Assume that the show will sell out. How many of each ticket must be sold for the revenue to be $637,000?

Answer 1

Kellie:

 

You have two equations:

 

x + y = 12500  (the total seats)

 

44x + 73y = 637000 (required revenue)

 

Method of elimination is easier.  From the first  you get y = 12500 - x.  Substitute in the second.

 

44x + 73(12500 - x) = 637000.

 

Solve for x and then get y as 12500 - x.

 

Dr. G.