Question

An arena that hosts sporting events and concerts has two sections for 2 levels of seating. For a basketball game seats in Section A cost $200 and seats in section B cost $100. The arena holds 10,000 seats and the game is sold out. If the total revenue from ticket sales is $1,150,000, determine the number of seats in each section.

Start by assigning your variables. Then write your system of equations. Solve using substitution or elimination. Show all work for thissystem of 2 equations.

Answer 1

Let number of seat in section A = x

number of seat in section B = y

Since arena holds 10,000 seats, set up first equation as

x+y= 10000

Since, total revenue from ticket sales is $1,150,000, set up second equation as

200x +100y= 1150000

Solve the eqaution using elimination method

Multiply the 1st equation by 200

200x+200y=2000000
200x+100y=1150000

Subtract the 2nd equation from the 1st equation

200y -100y =2000000 -1150000

100y =850000

y=850000/100

y=8500

From equation 1)

x =10000 -8500 =1500

Hence

number of seat in section A = 1500

number of seat in section B = 8500