SOLUTION: A civic center auditorium has three types of seating front floor rear floor and balcony. Front floor tickets cost $40 while rear floor tickets cost $30, and balcony tickets cost $2
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Question 223736: A civic center auditorium has three types of seating front floor rear floor and balcony. Front floor tickets cost $40 while rear floor tickets cost $30, and balcony tickets cost $20 each. If 225 tickets are sold and receipts total $7000 find the number of ticket sold for each type of seating when there are twice as many front floor tickets sold as rea floor tickets.
Here is what I have..x+y+z=225
40x+30y+20z=7000
2y=z..now what? Thanks for your help! Answer by MLipsky(9) (Show Source):
You can put this solution on YOUR website! You are off to a really good start. One small correction: I think your third equation should be:
Let's see if that makes sense. There are twice as many front floor tickets. So, "x" is the larger number. My formulas says "2 times larger number equals smaller number". No! The formula is still wrong. It should be:
So, using your equations, that gives us:
This looks like a system of 3 equations, with 3 unknowns. So we can solve it that way. But wait! Look at that third equation. If we start plugging it in to the other two, this whole problem gets a LOT easier.
Now, we only have 2 variables! Very cool.
Simplify first equation:
Simplify second equation: (divided by 10)
Now we have 2 equations. Let's solve by substitution. Since we can easily solve for "z" in the first equation:
we might as well substitute that into the second equation: (distributed 2) (combined like terms "y") (subtracted 450 from both sides) (divided both sides by 5)
Let's start using the other formulas to help us get "x" and "z". (previous formula) That was fast!
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