How Many of Each Ticket Were Sold?

Date: 09/06/2001 at 02:59:52
From: Sarah Kromer
Subject: Turning a word problem into an equation

Five hundred tickets were sold for a play, for $8 at the lower level 
and $6 at the upper level, totaling $3600. How many of each were sold?

I am having trouble putting this into an equation.

    (8x)+ (6Y) = 500

or (8x) + (6y) = 3600

I think it is the latter but I 'm getting stuck on where to go next.

I don't seem to have such a problem working out equations but when it 
comes to some - not all - word problems I experience a block.

Please help. Thank you.
Sarah

Date: 09/06/2001 at 10:49:45
From: Doctor Peterson
Subject: Re: Turning a word problem into an equation

Hi, Sarah.

An important part of writing an equation for a word problem is to be 
aware of exactly what everything means. That starts with writing down 
explicitly what your variables mean:

    x = number of lower level tickets sold
    y = number of upper level tickets sold

Now you can write expressions corresponding to particular phrases used 
in the problem, or to concepts implied by the problem; again, be as 
clear as possible:

    8x = cost in dollars for all lower level tickets sold
    6y = cost in dollars for all upper level tickets sold

Now the total cost of ALL the tickets is the sum of these:

    8x + 6y = cost in dollars of all tickets sold

Now that we see just what this expression means, we know that it has 
to be equal to the total cost, $3600:

    8x + 6y = 3600

We have one equation and two unknowns; that's not enough in general to 
solve the problem. But there's a piece of information we haven't used 
yet. Can you see how

    500 = total number of tickets sold

can be related to the variables x and y? That will give you a second 
equation; you can solve that for y, and then replace y in the first 
equation with the resulting expression in order to solve the problem.

I hope this helps. An orderly approach can help a lot in cutting 
through the complexities of the English language, as well as those of 
math.

- Doctor Peterson, The Math Forum
  http://mathforum.org/dr.math/