document.write( "Question 189726: Sam found a number of nickels, dimes, and quarters in his room. He found 6 more dimes than nickels but three times as many quarters as dimes. The total value of the coins was $11.40. how many coins of each type did Sam find? \n" ); document.write( "

Algebra.Com's Answer #142371 by josmiceli(19441) $\"\"$ $\"About$

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Let $\"n\"$ = number of nickels
\n" ); document.write( "Let $\"d\"$ = number of dimes
\n" ); document.write( "Let $\"q\"$ = number of quarters
\n" ); document.write( "given:
\n" ); document.write( "(1) $\"d+=+n+%2B+6\"$
\n" ); document.write( "(2) $\"q+=+3d\"$
\n" ); document.write( "(3) $\"5n+%2B+10d+%2B+25q+=+1140\"$ (in cents)
\n" ); document.write( "---------------------------
\n" ); document.write( "From (1),
\n" ); document.write( " $\"n+=+d+-+6\"$
\n" ); document.write( "Now I can rewrite (3)
\n" ); document.write( "(3) $\"5%2A%28d+-+6%29+%2B+10d+%2B+25%2A3d+=+1140\"$
\n" ); document.write( " $\"5%2A%28d+-+6%29+%2B+10d+%2B+25%2A3d+=+1140\"$
\n" ); document.write( " $\"5d+-+30+%2B+10d+%2B+75d+=+1140\"$
\n" ); document.write( " $\"90d+=+1140+%2B+30\"$
\n" ); document.write( " $\"90d+=+1170\"$
\n" ); document.write( " $\"d+=+13\"$
\n" ); document.write( "and from (1),
\n" ); document.write( " $\"n+=+d+-+6\"$
\n" ); document.write( " $\"n+=+13+-+6\"$
\n" ); document.write( " $\"n+=+7\"$
\n" ); document.write( "From (2),
\n" ); document.write( " $\"q+=+3d\"$
\n" ); document.write( " $\"q+=+3%2A13\"$
\n" ); document.write( " $\"q+=+39\"$
\n" ); document.write( "Sam found 7 nickels, 13 dimes, and 39 quarters
\n" ); document.write( "check answer:
\n" ); document.write( "(3) $\"5n+%2B+10d+%2B+25q+=+1140\"$
\n" ); document.write( " $\"5%2A7+%2B+10%2A13+%2B+25%2A39+=+1140\"$
\n" ); document.write( " $\"35+%2B+130+%2B+975+=+1140\"$
\n" ); document.write( " $\"1140+=+1140\"$
\n" ); document.write( "OK \n" ); document.write( "

\n" );