document.write( "Question 297266: What are the algebraic formulas for this (in a collection of nickels, dimes, and quarters, there are twice as many dimes as nickels and 3 fewer quarters than dimes. if the total value is $4.50 how many of each coin are there) \n" ); document.write( "

Algebra.Com's Answer #214077 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( " $\"d+=+2n\"$
\n" ); document.write( " $\"q+=+d+-+3\"$
\n" ); document.write( " $\"5n+%2B+10d+%2B+25q+=+450\"$ (in cents)
\n" ); document.write( "--------------------------
\n" ); document.write( "This is 3 equations and 3 unknowns, so it's solvable
\n" ); document.write( "By substitutions:
\n" ); document.write( " $\"5n+%2B+10d+%2B+25%2A%28d+-+3%29+=+450\"$
\n" ); document.write( "And, substituting again:
\n" ); document.write( " $\"5%2A%28d%2F2%29+%2B+10d+%2B+25%2A%28d+-+3%29+=+450\"$
\n" ); document.write( " $\"5d%2F2+%2B+10d+%2B+25d+-+75+=+450\"$
\n" ); document.write( " $\"5d+%2B+20d+%2B+50d+-+150+=+900\"$
\n" ); document.write( " $\"75d+=+1050\"$
\n" ); document.write( " $\"d+=+14\"$
\n" ); document.write( "and, since
\n" ); document.write( " $\"q+=+d+-+3\"$
\n" ); document.write( " $\"q+=+11\"$
\n" ); document.write( "and
\n" ); document.write( " $\"n+=+d%2F2\"$
\n" ); document.write( " $\"n+=+7\"$
\n" ); document.write( "There are 14 dimes, 11 quarters, and 7 nickels
\n" ); document.write( "check:
\n" ); document.write( " $\"5n+%2B+10d+%2B+25q+=+450\"$
\n" ); document.write( " $\"5%2A7+%2B+10%2A14+%2B+25%2A11+=+450\"$
\n" ); document.write( " $\"35+%2B+140+%2B+275+=+450\"$
\n" ); document.write( " $\"450+=+450\"$
\n" ); document.write( "OK
\n" ); document.write( " \n" ); document.write( "

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