Number of Quarters

Date: 9/11/96 at 19:32:28
From: Michael F. Biondi
Subject: Number of Quarters

Dear Dr. Math,

   How do I write an algebraic equation for the following problem? 

Tony has eleven more nickels than quarters. How many quarters does he 
have if the total value of his coins is $2.65?

I am stumped on this question. Thanks for any help you can give me.
     Eliza

Date: 9/12/96 at 14:4:27
From: Doctor Mike
Subject: Re: Number of Quarters

Hi Eliza,

Letting q be the number of quarters is a good start.  The total
amount of money for q quarters is 25*q cents.  The problem says
that he also has q+11 nickels.  The total amount of money for q+11
nickels is 5*(q+11) cents.  Now the other fact in the problem is
that the total money (from the value of the quarters and from the
value of the nickels all together) is 265 cents.  So, one way to
write the equation would be: 
  
      "money for q quarters" + "money for q+11 nickels"  =  265
  
Now rewrite this using just algebra expressions without words and
you have it.  If there is still something you don't understand just
write back. (By the way, the reason I used cents instead of dollars
was to avoid working with decimals.  Whole numbers representing cents
are easier to work with I think.  I also use cents when I balance my
checking account register each month for the same reason.)
  
I hope this helps.  
  
-Doctor Mike,  The Math Forum 
 Check out our web site!  http://mathforum.org/dr.math/   

Date: 9/12/96 at 10:35:43
From: Doctor Robert
Subject: Re: Number of Quarters

If Tony has Q quarters as you say, then he must have Q+11 nickels 
because the problem says so.  Now, what is the value of his coins.  
Each quarter is worth $.25.  Since he has Q quarters he must have 
(.25)Q dollars in quarters.  Since each nickel is worth $.05, he must 
have (Q+11)(.05) dollars in nickels.  The total amount that he has is 
the sum of these two and is equal to $2.65.  So the equation becomes

 .25Q + .05(Q+11) = 2.65
        .3Q + .55 = 2.65
              .3Q = 2.10
                Q = 7

Tony has 7 quarters and 18 nickels.  Does it check?  7 quarters is 
worth $1.75 and 18 nickels is worth $.90.  They add up to $2.65!

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