document.write( "Question 517095: There are 223 coins total of quarters, dimes, and nickels. The total value of the coins is $20.10. How many coins do I have of each?
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Algebra.Com's Answer #344670 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
Let $\"q\"$ = number of quarters
\n" ); document.write( "Let $\"+d+\"$ = number of dimes
\n" ); document.write( "Let $\"+n+\"$ = number of nickels
\n" ); document.write( "given:
\n" ); document.write( "(1) $\"+q+%2B+d+%2B+n+=+223+\"$
\n" ); document.write( "(2) $\"+25q+%2B+10d+%2B+5n+=+2010+\"$ ( in cents )
\n" ); document.write( "-------------
\n" ); document.write( "Multiply both sides of (1) by $\"5\"$
\n" ); document.write( "and subtract (1) from (2)
\n" ); document.write( "(2) $\"+25q+%2B+10d+%2B+5n+=+2010+\"$
\n" ); document.write( "(1) $\"+-5q+-+5d+-+5n+=+-1115+\"$
\n" ); document.write( " $\"+20q+%2B+5d+=+895+\"$
\n" ); document.write( " $\"+5d+=+895+-+20q+\"$
\n" ); document.write( " $\"+d+=+179+-+4q+\"$
\n" ); document.write( "---------------
\n" ); document.write( "Suppose there are 100 dimes
\n" ); document.write( " $\"+100+=+179+-+4q+\"$
\n" ); document.write( " $\"+4q+=+79+\"$ ( doesn't work, $\"d\"$ has to be odd)
\n" ); document.write( "--------
\n" ); document.write( "107 dimes:
\n" ); document.write( " $\"+107+=+179+-+4q+\"$
\n" ); document.write( " $\"+4q+=+72+\"$
\n" ); document.write( " $\"+q+=+18+\"$
\n" ); document.write( " $\"+107+%2B+18+%2B+n+=+223+\"$
\n" ); document.write( " $\"+n+=+98+\"$
\n" ); document.write( " $\"+25%2A18+%2B+10%2A107+%2B+5%2A98+=+450+%2B+1070+%2B+490+\"$
\n" ); document.write( " $\"+2010+\"$
\n" ); document.write( "---------
\n" ); document.write( "Wow! That was just a guess.
\n" ); document.write( "18 quarters, 107 dimes and 98 nickels \n" ); document.write( "

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