Software Sales

Date: 02/01/97 at 11:07:47
From: frank kreager
Subject: Software Sales

Hi,

I am doing word problems and am having a lot of trouble putting them 
into mathematical equations. Once I get the mathematical equation, I 
don't have any difficulties.
  
For instance: The three best selling software applications at one 
computer store are priced as follows: spreadsheet $150, database
$195, word processing, $210. Spreadsheet and database programs are 
sold in equal numbers, but 15 more word processing applications are 
sold than the other two combined. The three applications together 
generated sales of $72,000. How many spreadsheets are sold?

I would appreciate any assistance you can give me on how to transfer 
word problems into mathematical equations.

Thanks

Date: 02/03/97 at 21:45:58
From: Doctor Wallace
Subject: Re: Software Sales

Hi Frank!

Translating English to math gets easier the more you do it - you 
eventually get used to the phrases used.  

I can offer some general help: 

When you see                    It usually means
-------------                  --------------------
more than, sum, total, combined       +
less than, difference of              -
of, product                           x 
is, the same as, equal to             =

Let's go through your problem step by step and maybe it will shed some 
light on the process.

The first thing to do is write down what you know:

- Cost of spreadsheet program: $150
- Cost of database program: $195
- Cost of word processing program: $210
- Number of spreadsheet programs sold = number of database programs 
  sold
- 15 more word processing programs are sold than the number of 
spreadsheet and database programs sold

Since the number of spreadsheet programs sold is equal to the number 
of database programs sold, we will let X equal the number of EACH that 
is sold. We know that 15 more word processing programs are sold than 
the other two combined.  To translate this into English, we first need 
to ask what is the "other two combined". It's simply the total number 
of spreadsheet and database programs sold.  This is equal to X + X, 
which is the same as 2X.  If 15 more word processing programs than 
this are sold, then the number of word processing programs sold must 
be 2X + 15.

If we multiply the number of each program sold times the cost of each 
program, that gives the amount of money made from each program.  So, 
if we add those values together for each of our three programs, we 
should get the total sales, which we are told are $72,000.

Sales from spreadsheet programs: 150X
Sales from database programs: 195X
Sales from word processing programs: 210(2X + 15)

If we add these three things up and set them equal to $72,000, then we 
can solve for X, which is the total number of spreadsheet programs 
sold.  This is the answer that we are supposed to find.  It also 
happens to be the total number of database programs sold. Our equation 
is:

72,000 = 150X + 195X + 210(2X + 15)  
72,000 = 150X + 195X + 420X + 3150     Distribute the 210
72,000 = 765X + 3159                   Add like terms with X's in them
68,850 = 765X                          Subtract 3150 from each side
90 = X                                 Divide each side by 765

This means that 90 spreadsheet programs are sold.  

I hope this helps, Frank.  If you need more assistance, don't hesitate 
to write back!

-Doctors Rachel and Wallace,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/