Question for Intermediate Algebra

Question

In a baseball stadium, there are three types of seats available. Box seats are $10, reserved seats are $7, and lawn seats are $4. The stadium capacity is 4000. If all the seats are sold, the total revenue to the club is $28,030. If one half of the box seats sold, one half of the reserved seats are sold, and all the lawn seats are sold, the total revenue is $17,095. How many of each kind of seat are there?

Answer 1

Hi Ronnie, set this up as a system of three equations. Let b represent the box seats, r represent the reserved seats, and l represent the lawn seats.

 

Equation 1, total seats:

 

b + r + l = 4000

 

Equation 2, total revenue:

 

10b + 7r + 4l = 28030

 

Equation 3, partial revenue:

 

10 * (.5b) + 7 * (.5r) + 4l = 17095

 

You now have three equations in three unknowns. 

 

    b  +      r   +  l   =  4000

10b  +    7r   + 4l  = 28030

 5b   +  3.5r  + 4l  = 17095

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Use elimination to solve for b, r, and l. I would suggest to start by eliminating the b variable.

 

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