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How Many of Each Ticket Were Sold?

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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.

Sarah
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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

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/
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Associated Topics:
Middle School Algebra
Middle School Word Problems

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