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

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• May 3rd 2011, 09:34 PM
DjNito
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!! • May 3rd 2011, 09:47 PM pickslides 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... Quote: 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?
• May 3rd 2011, 09:56 PM
earboth
Quote:

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 $15,420. How many of each kind of seat are there? I been trying for litterly 2 hours and I can't seem to figure it out. I've tryed making a System of linear equations in 3 variables and I can't figure it out. Any help would be awesome. Thanks in advance guys!! This is a quite misterious question ... 1. Let b denote the number of boxed seats, r denote the number of reserved seats, l denote the number of lawn seats. Then you can set up a system of simultaneous equations:$\displaystyle \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
• May 3rd 2011, 10:03 PM
DjNito
Quote:

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