# Thread: Worded problem - finding and solving a system of linear equations.

1. ## Worded problem - finding and solving a system of linear equations.

Alright I'm sure I'm posting this in the right area if not I am truly sorry. So I have come across a problem that me and my brother have been trying to solve for a while and cannot figure it out would love some help. The problem is:

In a baseball stadium, there are three types of seats available. Box seats are $9, Reserved seats are$6, and lawn seats are $4. The stadium capacity is 3900. If all seats are sold, the total revenue to the club is$24,600. If one half of the box seats sold, one half of the reserved seats sold, and all the lawn seats are sold, the total revenue is $15,420. How many of each kind of seat are there? I been trying for litterly 2 hours and I can't seem to figure it out. I've tryed making a System of linear equations in 3 variables and I can't figure it out. Any help would be awesome. Thanks in advance guys!! 2. Let B = Box seats, R = Reserved seat and L = Lawn seats. Here's some equations B+R+L=3900 and 9B+6R+4L=24600 All you need now is one more equation and you can solve the system, look here... Originally Posted by DjNito If one half of the box seats sold, one half of the reserved seats sold, and all the lawn seats are sold, the total revenue is$15,420. How many of each kind of seat are there?
Can you make an equation from that?

3. Originally Posted by DjNito
Alright I'm sure I'm posting this in the right area if not I am truly sorry. So I have come across a problem that me and my brother have been trying to solve for a while and cannot figure it out would love some help. The problem is:

In a baseball stadium, there are three types of seats available. Box seats are $9, Reserved seats are$6, and lawn seats are $4. The stadium capacity is 3900. If all seats are sold, the total revenue to the club is$24,600. If one half of the box seats sold, one half of the reserved seats sold, and all the lawn seats are sold, the total revenue is \$15,420. How many of each kind of seat are there?

I been trying for litterly 2 hours and I can't seem to figure it out. I've tryed making a System of linear equations in 3 variables and I can't figure it out. Any help would be awesome.

This is a quite misterious question ...

1. Let
b denote the number of boxed seats,
r denote the number of reserved seats,
l denote the number of lawn seats.

Then you can set up a system of simultaneous equations:

$\left|\begin{array}{rcl}b+r+l&=&3900 \\ 9b+6r+4l&=&24600 \\ 4.5b+3r+4l&=&15420\end{array}\right.$

2. The solution of this system of equations is: (b, r, l) = (1980, -300, 2280)

But I can't imagine -300 seats. Must be quite a big hole in the stadium.

EDIT: Sorry I made a typo. The system of equations I set up has a unique solution

4. Originally Posted by pickslides
Can you make an equation from that?
I actually did make an equation out of that thanks for the help i used

1/2(9b)+1/2(6r)+4x=15420

When I solved everything I got

Box = 1440
Reserved = 900
Lawn = 1560

thanks for the help guys