Math question - MBA Level

Question

A hockey arena has 2,500 seats in the preferred red sections near centre ice and 4,500 seats in the less desirable blue sections. At regular season prices, a sell-out would generate ticket revenue of $50,250 for a single game. Ticket prices are raised by 20% in the “blues” and 30% in the “reds” for the playoffs. Ticket revenue from a playoff sell-out would be $62,400. What are the ticket prices for the red section during the playoffs? Calculate to the nearest cent. Fill in the answer using numbers only, separated by commas, with a decimal point, as needed. Do not use letters or any other symbols, including a dollar sign. If you fail to follow these instructions, your answer will be incorrect

Answer 1

Let x = the cost of red seat and y = the cost of a blue seat.  We have two unknowns, x and y, so we need to find two equations to solve for them.  The revenue equation for regular season is:

 

Revenue = (number of red seats) (cost per red seat) + (number of blue seats) (cost per blue seat)

$50,250 = 2500x + 4500y

 

For the playoffs ticket prices are raised 30% for the reds, so each red seat now costs 1.3x.  The blue seat process are raised by 20% so each blue seat now costs 1.2y.  The revenue equation for the playoffs is:

 

Revenue = 2500(1.3x) + 4500(1.2y)

$62,400 = 3250x + 5400y

 

We now have our system of two linear equations:

 

$50,250 = 2500x + 4500y

$62,400 = 3250x + 5400y

 

Solve by substitution or elimination.