document.write( "Question 300978: I need help with this word math problem.
\n" ); document.write( "In a collection of nickels, dimes, and quarters, there are twice as many dimes as nickels, and fewer quarters than dimes. If the total value of the coins is $4.50, how many of each type of coin are there? \n" ); document.write( "

Algebra.Com's Answer #215858 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
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( " $\"5n+%2B+10d+%2B+25q+=+450\"$ (in cents)
\n" ); document.write( " $\"d+=+2n\"$
\n" ); document.write( " $\"q+%3C+d\"$
\n" ); document.write( "---------
\n" ); document.write( "By substitution:
\n" ); document.write( " $\"5n+%2B+10%2A%282n%29+%2B+25q+=+450\"$
\n" ); document.write( " $\"25n+%2B+25q+=+450\"$
\n" ); document.write( " $\"n+%2B+q+=+18\"$
\n" ); document.write( " $\"d%2F2+%2B+q+=+18\"$
\n" ); document.write( "I know that $\"q%3C18\"$ , since quarters must add up to less than $4.50
\n" ); document.write( "If $\"q%3Cd\"$ then, suppose $\"q+=+11\"$ , $\"d\"$ could be $\"10\"$
\n" ); document.write( "That's $2.75 plus $1.00 = $3.75. If there are twice as many dimes as
\n" ); document.write( "nickels, $\"n+=+5\"$ , totaling $.25
\n" ); document.write( "$3.75 + $.25 = $4.00
\n" ); document.write( "My next guess is $\"q+=+13\"$ , $\"d+=+12\"$ , $\"n+=+6\"$
\n" ); document.write( "You can go on from here, since you get the idea \n" ); document.write( "

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