<PRE><B>Question 7700</B>
We have two facts to start with&lt;br&gt;

1) the number of nickels and the number of dimes add up to 35&lt;br&gt;
2) the value of the nickels and dimes add up to $3.30&lt;br&gt;
&lt;br&gt;
Let&#39;s call the number of nickels &lt;i&gt;n&lt;/i&gt; and the number of dimes &lt;i&gt;d&lt;/i&gt;. The number of coins add up to 35 and the value of the nickels is $0.05n and the value of the dimes is $0.10d. We can convert the two facts to a mathematical representation as follows:&lt;br&gt;
&lt;br&gt;
1) n + d = 35&lt;br&gt;
2) $0.05n + $0.10d = 3.30&lt;br&gt;
&lt;br&gt;
Subtract n from both sides of the first equation to get&lt;br&gt;
d + n - n = 35 - n&lt;br&gt;
d = 35 - n&lt;br&gt;
&lt;br&gt;
Now substitute d = 35 - n into the second equation:&lt;br&gt;
0.05n + 0.10(35 - n) = 3.3&lt;br&gt;
0.05n + 3.5 - 0.10n = 3.3&lt;br&gt;
3.5 - 0.05n = 3.3&lt;br&gt;
&lt;br&gt;
Subtract 3.3 from either side&lt;br&gt;
3.5 - 0.05n - 3.3 = 3.3 - 3.3&lt;br&gt;
0.2 - 0.05n = 0&lt;br&gt;
&lt;br&gt;
Add 0.05n to either side to get&lt;br&gt;
0.2 - 0.05n + 0.05n = 0.05n&lt;br&gt;
0.2 = 0.05n&lt;br&gt;
&lt;br&gt;
divide both sides by 0.05 to get:&lt;br&gt;
{{{0.2/0.05}}}={{{0.05n/0.05}}}&lt;br&gt;
&lt;br&gt;
So, n = 4. Since d + n = 35 and n = 4, we know d + 4 = 35. Subtract 4 from either side to get d = 31.&lt;br&gt;
&lt;br&gt;
The answer is 4 nickels and 31 dimes.&lt;br&gt;
To see that this is true, figure out how much 4 nickels and 31 dimes are worth. The 4 nickels add up to $0.20 and the 31 dimes add up to $3.10, the nickels and dimes add up to $3.30. This is exactly what the problem says.


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