document.write( "Question 289014: Mike has 19 coins (nickels, dimes, and quarters) in his piggy bank with a total value of $2.35. There are two more dimes than nickels. How many of each type of cion does mike have?\r
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Algebra.Com's Answer #209447 by Fombitz(32388)\"\" \"About 
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N-number of nickels, worth 5 cents each
\n" ); document.write( "D-number of dimes, worth 10 cents each
\n" ); document.write( "Q-number of quarters, worth 25 cents each
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\n" ); document.write( "\"Mike has 19 coins\"
\n" ); document.write( "1.\"N%2BD%2BQ=19\"
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\n" ); document.write( "\"a total value of $2.35 (235 cents)\"
\n" ); document.write( "2.\"5N%2B10D%2B25Q=235\"
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\n" ); document.write( "\"two more dimes than nickels\"
\n" ); document.write( "3.\"D=N%2B2\"
\n" ); document.write( "Substitute eq. 3 into 1 and 2.
\n" ); document.write( "1.\"N%2BD%2BQ=19\"
\n" ); document.write( "\"N%2B%28N%2B2%29%2BQ=19\"
\n" ); document.write( "We'll call this eq. 4.
\n" ); document.write( "4.\"2N%2BQ=17\"
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\n" ); document.write( "2.\"5N%2B10D%2B25Q=235\"
\n" ); document.write( "\"5N%2B10%28N%2B2%29%2B25Q=235\"
\n" ); document.write( "\"5N%2B10N%2B20%2B25Q=235\"
\n" ); document.write( "We'll call this eq. 5.
\n" ); document.write( "5.\"15N%2B25Q=215\"
\n" ); document.write( "Now use eq. 4, to get Q in terms of N and substitute into eq. 5.
\n" ); document.write( "4.\"2N%2BQ=17\"
\n" ); document.write( "\"Q=17-2N\"
\n" ); document.write( "5.\"15N%2B25Q=215\"
\n" ); document.write( "\"15N%2B25%2817-2N%29=215\"
\n" ); document.write( "\"15N%2B425-50N=215\"
\n" ); document.write( "\"-35N=-210\"
\n" ); document.write( "\"N=6\"
\n" ); document.write( "Now work backwards,
\n" ); document.write( "\"Q=17-2N\"
\n" ); document.write( "\"Q=17-2%286%29=17-12=5\"
\n" ); document.write( "And finally,
\n" ); document.write( "\"D=N%2B2\"
\n" ); document.write( "\"D=6%2B2=8\"
\n" ); document.write( "6 nickels, 8 dimes, and 5 quarters.
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