Buying Stamps

Date: 08/21/97 at 13:11:47
From: Anonymous
Subject: Buying Stamps

Dr. Math,

I am an adult who is taking a correspondence course in Algebra I.  
I have the following question, and the textbook has not addressed this 
kind of problem. If you could please guide me through the steps of 
solving it, I would be very appreciative.

A man purchases some .02 and some .15 cent stamps at the same time.  
He pays $1.56 for all the stamps.  There are 10 more .02 stamps than 
.15 stamps.  How many of each kind did he buy?

Thanks,
Sherell

Date: 08/22/97 at 15:04:27
From: Doctor Beth
Subject: Re: Buying Stamps

Okay, we'll have to decide to let a variable equal something, perhaps 
the number of .15 stamps.  

If x is the number of .15 stamps we buy, then the number of .02 stamps 
is 10 more, so it's x + 10.  

When the man purchases the stamps, he spends $1.56, but we also know 
that he spends .15x + .02(x+10), because the amount spent is the 
number of stamps times the price of each stamp. So now we have the 
equation

   1.56 = .15x + .02(x+10)     
                               To solve for x, first I'll 
                               multiply and get
   1.56 = .15x + .02x + .2     
                               Now I'll combine .15x and .02x
                               to get .17x, and subtract the 
                               .2 from both sides, to get
   1.36 = .17x                 

Dividing both sides by .17 gives us 

      8 = x

So now we know that 8 = x, but we're not quite done - we have to make 
sure that we're answering the question in the problem. Since x was the 
number of .15 stamps, the man purchased 8 of the .15 stamps. The 
number of .02 stamps that he bought was x+10, so it must be 18.

You can even check your answer by seeing that if you buy 8 stamps at 
15 cents each, and then buy 18 stamps that each cost 2 cents, that you 
spend $1.56.

Good luck in your course!

-Doctor Beth,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/