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Organizing the Information in an Algebraic Word Problem

Date: 09/05/2007 at 11:31:12
From: Barbara
Subject: How many games did each of these three teams win?

In a baseball league of ten teams, Jennifer's team is currently in 
first place with forty wins.  Jordan's team is eight games behind
Jennifer's team.  Aaron's team is eight games behind Jordan's team.  
In the next thirty-one games, Jordan's team won fourteen more than the
number of games won by Jennifer's team.  Aaron's team won sixteen less
than the number of games won by Jordan's team.  Three times the number
of games won by Jennifer's team, during these thirty-one games, was
thirty-two more than the number of games won by Aaron's.  The sum of
the games won by these three teams after the complete season is 153.
How many games did each of these three teams win?  

I find the way that they are explaining it very confusing. Also I
can't tell which information is necessary and which is not.

I tried to make formulas to solve it but than I can't tell which
information I don't need, and can't seem to make one that will give me
an answer. I don't even know if a formula is the way to solving it.



Date: 09/05/2007 at 16:27:29
From: Doctor Ian
Subject: Re: How many games did each of these three teams win?

Hi Barbara,

Let's just write down what we know, and what we'd like to find out.

>In a baseball league of ten teams, Jennifer's team is currently in
>first place with forty wins. 

We can use a table to help keep things straight:

               Now
  
  Jennifer     40

>Jordan's team is eight games behind Jennifer's team. 

               Now
  
  Jennifer     40
  Jordan       32

>Aaron's team is eight games behind Jordan's team. 

               Now
  
  Jennifer     40
  Jordan       32
  Aaron        24

>In the next thirty-one games, Jordan's team won fourteen more than
>the number of games won by Jennifer's team. 

Let's use x to represent the number of games won by Jennifer's team:

               Now     Later
  
  Jennifer     40      x
  Jordan       32      x + 14
  Aaron        24

>Aaron's team won sixteen less than the number of games won by
>Jordan's team. 

               Now     Later
  
  Jennifer     40      x
  Jordan       32      x + 14
  Aaron        24     (x + 14) - 16   ->  or just x - 2


>three times the number of games won by Jennifer's team, during these
>thirty-one games, was thirty-two more than the number of games won by
>Aaron's. 

What does this mean?  Let's translate it, using the expressions from
our table:

  three times the number of games won by Jennifer's team, 
  during these thirty-one games, 
  was thirty-two more than the number of games won by Aaron's. 

  three times x, 
  was thirty-two more than (x-2).


  3x = (x - 2) + 32

So at this point, you have enough information to find x.  

>the sum of the games won by these three teams after the complete
>season is 153.  how many games did each of these three teams win?  

Once you know what x is, can you see how to find this? 

>I find the way that they are explaining it very confusing. Also i
>can't tell which information is necessary and which is not.

In general, assume something they tell you is necessary, until you
know for sure that it's not.  Sometimes something that seems pointless
can turn out to be important later on, especially in a multi-part
problem like this one.  

For example, I didn't really need the first column in the table to
answer the first question!  But it will come in pretty handy for the
second. 

>i tried to make formulas to solve it but than i can't tell which
>information i don't need, and can't seem to make one that will give
>me an answer. I don't even know if a formula is the way to solving >it.

It's hardly ever the case that there is a "formula" for solving a
problem.  That ends around 5th grade, where a typical problem will
require you to do one, or maybe two, calculations to get the answer. 

For more complicated problems like this one, the point is to give you
practice at systematically working (and thinking!) your way through
problems you haven't seen before.  If a formula were available, there
would be no point in asking you to solve the problem. 

Does that make sense?  Let me know if you need more help.

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



Date: 09/05/2007 at 16:49:19
From: Barbara
Subject: Thank you (How many games did each of these three teams win?)

thank you so much for helping me.^-^ i really appreciate all your 
help.  when you explained it i actually understood it.  so thank you 
for working so hard to help me.  you're the best! :D
Associated Topics:
Middle School Word Problems

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