<PRE><B>Question 196326</B>
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Let &lt;b&gt;&lt;i&gt;n&lt;/i&gt;&lt;/b&gt; represent the number of nickels.


Let &lt;b&gt;&lt;i&gt;d&lt;/i&gt;&lt;/b&gt; represent the number of dimes.


Let &lt;b&gt;&lt;i&gt;q&lt;/i&gt;&lt;/b&gt; represent the number of quarters.


Ok, that&#39;s three variables -- seems like a good start.  Now let&#39;s see what we can do about three equations.


We know that there are 19 coins in all, so:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ n + d + q = 19]


That&#39;s our first equation.


And we know that the number of dimes is three less than the sum of the numbers of nickels and quarters, so:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ d = n + q - 3]


And that&#39;s our second equation.


We also know that the total amount of money is $2.35, which can also be expressed as 235 cents.  Furthermore, nickels are worth 5 cents each, dimes 10 cents each, and quarters are 25 cents each.  So the values of her coins are:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 5n] is the value of the nickels


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 10d] is the value of the dimes, and


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 25q] is the value of the quarters; all values expressed in cents, so:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 5n + 10d + 25q = 235]


which is the third equation.


Solve the system for &lt;b&gt;&lt;i&gt;n&lt;/i&gt;&lt;/b&gt;, &lt;b&gt;&lt;i&gt;d&lt;/i&gt;&lt;/b&gt;, and &lt;b&gt;&lt;i&gt;q&lt;/i&gt;&lt;/b&gt; and you will have your answer.


John
*[tex \LARGE e^{i\pi} + 1 = 0]
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