Question 869166
Let's say we represent the number of dimes by {{{d}}} and the number of quarters by {{{q}}}
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We now that the total number should add up to 84, which can be written like <br>
{{{d + q =84}}} (1)
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Additionally we know that 
&nbsp;&nbsp;- 1 dime values 10 cents
&nbsp;&nbsp;- 1 quarter values 25 cents
&nbsp;&nbsp;- the total value of our piggy back is 16,05 dollar or <b>1605</b> cents 
<br>So we can write:<br>

&nbsp;&nbsp;{{{10d + 25q = 1605}}} (2)
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This gives us 2 equations (1) and (2).<br>
Equation (1) can be rewritten like so:
<br>&nbsp;&nbsp;{{{d=84-q}}}
<br>Substituting this into equation (2) gives:<br>
&nbsp;&nbsp;{{{(84-q)*10 + 25q=1605}}}<br>
&nbsp;&nbsp;{{{840-10q + 25q=1605}}}<br>
&nbsp;&nbsp;{{{15q=1605-840}}}<br>
&nbsp;&nbsp;{{{q=(1605-840)/15}}}
&nbsp;&nbsp;{{{q=51}}}
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Using this value in equation (1) gives us the number of dimes:
<br>&nbsp;&nbsp;{{{d=84-q}}}  ->   {{{d=84-51=33}}}<br>
So there are 51 quarters and 33 dimes in the piggy back.<br>
Check:
&nbsp;&nbsp;51 quarters + 33 dimes = 84 coins
&nbsp;&nbsp;with a total value of 51 x 25 cents + 33 x 10 cents = 1605 cents = 16,05 dollar