Inequalities and Linear Equations

Question

Receipts from a concert total is $12,000.The first floor seats $20 and the balcony seats were $15. If the number of those buying each kind of seat had been reversed, the total would have been $10,750. How many of each type of seat was sold?

Answer 1

Let x = the number of first floor seats

Let y = the number of balcony seats

20x + 15y = 12,000      Divide by 5 to get smaller numbers with which to work.

4x + 3y = 2400     Multiply by 4 to be able to solve using elimination

15x + 20y = 10,750      Divide by 5 again.

3x + 4y = 2150     Multiply by -3 to be able to solve using elimination.

16x + 12y = 9600

 -9x -12y = -6450

   7x        = 3150

            x = 450

4x + 3y = 2400

4(450) + 3y = 2400

1800 + 3y = 2400

3y = 600

y = 200

 

 

Answer 2

20F + 15B = 12000

 

15F + 20B = 10750

 

Multiplies the first equation by 15 and the second by -20

 

 300F + 225B = 180000

-300F - 400B = -215000

 

-175B = -35000

 

B  = 200

F = 450