document.write( "Question 266429: A group of nickels, dimes, and quarters is worth $9.50. There are two-thirds as many nickels as dimes and half as many dimes as quarters. How many quarters are there? \n" ); document.write( "

Algebra.Com's Answer #195778 by josmiceli(19441) $\"\"$ $\"About$

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$\"n\"$ = number of nickels
\n" ); document.write( " $\"d\"$ = number of dimes
\n" ); document.write( " $\"q\"$ = number of quarters
\n" ); document.write( "given:
\n" ); document.write( "(1) $\"5n+%2B+10d+%2B+25q+=+950\"$ (in cents)
\n" ); document.write( "(2) $\"n+=+%282%2F3%29%2Ad\"$
\n" ); document.write( "(3) $\"d+=+%281%2F2%29%2Aq\"$
\n" ); document.write( "-----------------
\n" ); document.write( "From (3)
\n" ); document.write( " $\"q+=+2d\"$
\n" ); document.write( "By substitution:
\n" ); document.write( "(1) $\"5%2A%282%2F3%29%2Ad+%2B+10d+%2B+25%2A%282d%29+=+950\"$
\n" ); document.write( " $\"%2810%2F3%29%2Ad+%2B+10d+%2B+50d+=+950\"$
\n" ); document.write( " $\"10d+%2B+30d+%2B+150d+=+2850\"$
\n" ); document.write( " $\"190d+=+2850\"$
\n" ); document.write( " $\"d+=+15\"$
\n" ); document.write( "From (3)
\n" ); document.write( " $\"q+=+2d\"$
\n" ); document.write( " $\"q+=+30\"$
\n" ); document.write( "There are 30 quarters
\n" ); document.write( "check answer:
\n" ); document.write( "(2) $\"n+=+%282%2F3%29%2Ad\"$
\n" ); document.write( " $\"n+=+%282%2F3%29%2A15\"$
\n" ); document.write( " $\"n+=+10\"$
\n" ); document.write( "and
\n" ); document.write( "(1) $\"5n+%2B+10d+%2B+25q+=+950\"$
\n" ); document.write( "(1) $\"5%2A10+%2B+10%2A15+%2B+25%2A30+=+950\"$
\n" ); document.write( " $\"50+%2B+150+%2B+750+=+950\"$
\n" ); document.write( " $\"950+=+950\"$
\n" ); document.write( "OK \n" ); document.write( "

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