document.write( "Question 239245: There are 15 coins consisting of nickels, dimes and quarters. Their total is $1.10. The is one less nickels than four times the dimes. How many of each coin are there? Equation needed. \n" ); document.write( "

Algebra.Com's Answer #175687 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) $\"5n+%2B+10d+%2B+25q+=+110\"$ (in cents)
\n" ); document.write( "(2) $\"n+=+4d+-+1\"$
\n" ); document.write( "There are 3 unknowns, and only 2 equations,
\n" ); document.write( "so it will take some extra work to solve
\n" ); document.write( "Substitute (2) into (1)
\n" ); document.write( " $\"5%2A%284d+-+1%29+%2B+10d+%2B+25q+=+110\"$
\n" ); document.write( " $\"20d+-+5+%2B+10d+%2B+25q+=+110\"$
\n" ); document.write( " $\"30d+%2B+25q+=+115\"$ cents
\n" ); document.write( "Now just use logic
\n" ); document.write( "There can't be 5 quarters, since that's more than $\"115\"$
\n" ); document.write( "There can't be 4 quarters, since
\n" ); document.write( " $\"30d+%2B+25%2A4+=+115\"$
\n" ); document.write( " $\"30d+%2B+100+=+115\"$
\n" ); document.write( " $\"30d+=+15\"$
\n" ); document.write( " $\"d+=+1%2F2\"$ (can't have 1/2 dime)
\n" ); document.write( "I'll try 3 quarters
\n" ); document.write( " $\"30d+%2B+25%2A3+=+115\"$
\n" ); document.write( " $\"30d+=+115+-+75\"$
\n" ); document.write( " $\"30d+=+40\"$
\n" ); document.write( " $\"d+=+4%2F3\"$ (can't have 4/3 dimes)
\n" ); document.write( "I'll try 2 quarters
\n" ); document.write( " $\"30d+%2B+25%2A2+=+115\"$
\n" ); document.write( " $\"30d+=+115+-+50\"$
\n" ); document.write( " $\"30d+=+65\"$
\n" ); document.write( " $\"d+=+13%2F6\"$ (can't have 13/6 dimes)
\n" ); document.write( "And 1 quarter
\n" ); document.write( " $\"30d+%2B+25%2A1+=+115\"$
\n" ); document.write( " $\"30d+=+90\"$
\n" ); document.write( " $\"d+=+3\"$
\n" ); document.write( "and, since
\n" ); document.write( "(2) $\"n+=+4d+-+1\"$
\n" ); document.write( " $\"n+=+4%2A3+-+1\"$
\n" ); document.write( " $\"n+=+11\"$
\n" ); document.write( "There is 1 quarter, 3 dimes, and 11 nickels
\n" ); document.write( "check:
\n" ); document.write( "(1) $\"5n+%2B+10d+%2B+25q+=+110\"$
\n" ); document.write( " $\"5%2A11+%2B+10%2A3+%2B+25%2A1+=+110\"$
\n" ); document.write( " $\"55+%2B+30+%2B+25+=+110\"$
\n" ); document.write( " $\"110+=+110\"$
\n" ); document.write( "OK \n" ); document.write( "

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