Word problems: A performance got $61800 for 3000 tickets.

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Nicky

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I need help getting started on this one:

A ballet performance brought in $61800 on the sale of 3000 tickets. If the tickets sold for $14 and $25, how many of each were sold?

I know that you have to somehow get it into a quadratic formula so that you will have two answers for x, but i'm not sure how to do that...
 
Re: Word problems: A performance got $61800 for 3000 tickets

Nicky said:
I know that you have to somehow get it into a quadratic [equation]....
Click to expand...
Why?

Pick a variable for the number of -- picking one randomly -- high-price tickets. Then how many cheap-seat tickets were sold?

Write an expression, in terms of the variable, for the income that was gained from the sale of high-price tickets. Write another expression, in terms of the one in the previous paragraph, for the income from the cheap-seat tickets.

Add the two income expressions, set equal to the given income total, and solve the linear equation for the variable.

If you get stuck, please reply showing how far you have gotten, starting with the variable you picked and what it stood for. Thank you.

Eliz.
 
Re: Word problems: A performance got $61800 for 3000 tickets

Nicky said:
I need help getting started on this one:

A ballet performance brought in $61800 on the sale of 3000 tickets. If the tickets sold for $14 and $25, how many of each were sold?

I know that you have to somehow get it into a quadratic formula so that you will have two answers for x, but i'm not sure how to do that...
Click to expand...

How about x + y = 30000 and 14x + 25y = 61,800, x and y being how many of each price were sold.
 
the variables...

okay, then would x equal the number of cheap tickets and 3000-x equal the other tickets? then the equation would be...gah, i'm not sure. the reason i'm so confused by this is because my teacher said that none of the word problems he was giving us would have two variables in them and that they all could be solved using only one.
 
Re: the variables...

Nicky said:
would x equal the number of cheap tickets and 3000-x equal the other tickets?
Click to expand...
Exactly.

Now: If you'd sold one cheap seat, how much did you get? How about if you'd sold 2? How about 3? How about x? This gives you the income expression for the cheap-seat tickets. Follow this reasoning to find the other income expression.

Eliz.
 
so the income expression for the cheap-seat tickets is x(x). and for the expensive seats it's x(3000-x)? then what do you set them equal to?
 
Re: the variables...

Nicky said:
okay, then would x equal the number of cheap tickets and 3000-x equal the other tickets? then the equation would be...gah, i'm not sure. the reason i'm so confused by this is because my teacher said that none of the word problems he was giving us would have two variables in them and that they all could be solved using only one.
Click to expand...
One variable IS all you need here:
x = $14 tickets; then 3000-x = $25 tickets; so your equation is:
14x + 25(3000-x) = 61800
Solve for x.
 
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