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!!

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?

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:



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

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