document.write( "Question 869166: you have a piggy bank containing a total of 84 coins in dimes and quarters. If the piggy bank contains $16.05, how many dimes are there in the piggy bank? \n" ); document.write( "

Algebra.Com's Answer #524063 by XilliX(3) $\"\"$ $\"About$

You can put this solution on YOUR website!
Let's say we represent the number of dimes by $\"d\"$ and the number of quarters by $\"q\"$
\n" ); document.write( "

\n" ); document.write( "We now that the total number should add up to 84, which can be written like

\n" ); document.write( " $\"d+%2B+q+=84\"$ (1)
\n" ); document.write( "

\n" ); document.write( "Additionally we know that
\n" ); document.write( "  - 1 dime values 10 cents
\n" ); document.write( "  - 1 quarter values 25 cents
\n" ); document.write( "  - the total value of our piggy back is 16,05 dollar or 1605 cents
\n" ); document.write( "
So we can write:
\r
\n" ); document.write( "\n" ); document.write( "   $\"10d+%2B+25q+=+1605\"$ (2)
\n" ); document.write( "

\n" ); document.write( "This gives us 2 equations (1) and (2).

\n" ); document.write( "Equation (1) can be rewritten like so:
\n" ); document.write( "
   $\"d=84-q\"$
\n" ); document.write( "
Substituting this into equation (2) gives:

\n" ); document.write( "   $\"%2884-q%29%2A10+%2B+25q=1605\"$

\n" ); document.write( "   $\"840-10q+%2B+25q=1605\"$

\n" ); document.write( "   $\"15q=1605-840\"$

\n" ); document.write( "   $\"q=%281605-840%29%2F15\"$
\n" ); document.write( "   $\"q=51\"$
\n" ); document.write( "

\n" ); document.write( "Using this value in equation (1) gives us the number of dimes:
\n" ); document.write( "
   $\"d=84-q\"$ -> $\"d=84-51=33\"$

\n" ); document.write( "So there are 51 quarters and 33 dimes in the piggy back.

\n" ); document.write( "Check:
\n" ); document.write( "  51 quarters + 33 dimes = 84 coins
\n" ); document.write( "  with a total value of 51 x 25 cents + 33 x 10 cents = 1605 cents = 16,05 dollar\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );