document.write( "Question 341924: Sarah has a coin collection of nickels, dimes, and quarters worth $15.75. She has 10 more dimes than nickels and twice as many quarters as dimes. How many coins of each does she have? \n" ); document.write( "

Algebra.Com's Answer #244793 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) $\"d+=+n+%2B+10\"$
\n" ); document.write( "(2) $\"q+=+2d\"$
\n" ); document.write( "(3) $\"5n+%2B+10d+%2B+25q+=+1575\"$ (in cents)
\n" ); document.write( "By substitution:
\n" ); document.write( "From(1)
\n" ); document.write( " $\"n+=+d+-+10\"$
\n" ); document.write( "(3) $\"5%2A%28d+-+10%29+%2B+10d+%2B+25q+=+1575\"$
\n" ); document.write( "By substitution again:
\n" ); document.write( "(3) $\"5%2A%28d+-+10%29+%2B+10d+%2B+25%2A2d+=+1575\"$
\n" ); document.write( " $\"5d+-+50+%2B+10d+%2B+50d+=+1575\"$
\n" ); document.write( " $\"65d+=+1625\"$
\n" ); document.write( " $\"d+=+25\"$
\n" ); document.write( "From (1):
\n" ); document.write( " $\"n+=+d+-+10\"$
\n" ); document.write( " $\"n+=+25+-+10\"$
\n" ); document.write( " $\"n+=+15\"$
\n" ); document.write( "From (2):
\n" ); document.write( " $\"q+=+2d\"$
\n" ); document.write( " $\"q+=+2%2A25\"$
\n" ); document.write( " $\"q+=+50\"$
\n" ); document.write( "She has 15 nickels, 25 dimes, and 50 quarters
\n" ); document.write( "check:
\n" ); document.write( "(3) $\"5n+%2B+10d+%2B+25q+=+1575\"$
\n" ); document.write( " $\"5%2A15+%2B+10%2A25+%2B+25%2A50+=+1575\"$
\n" ); document.write( " $\"75+%2B+250+%2B+1250+=+1575\"$
\n" ); document.write( " $\"1575+=+1575\"$
\n" ); document.write( "OK \n" ); document.write( "

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