document.write( "Question 318136: A collection of coins consists of nickels, dimes, and quarters. there are 4 less nickels than dimes. There are 26 coins in total. The total value of the collection is $3.10. Fine the number of each type of coin. \n" ); document.write( "

Algebra.Com's Answer #227772 by Fombitz(32388) $\"\"$ $\"About$

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Let N be the number of nickels, D dimes, Q quarters.
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\n" ); document.write( "\"There are 26 coins in total.\"
\n" ); document.write( "1. $\"N%2BD%2BQ=26\"$
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\n" ); document.write( "\"there are 4 less nickels than dimes\"
\n" ); document.write( "2. $\"N=D-4\"$
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\n" ); document.write( "\"The total value of the collection is $3.10\"
\n" ); document.write( "3. $\"5N%2B10D%2B25Q=310\"$
\n" ); document.write( "Substitute eq. 2 into eq. 1 and eq. 3,
\n" ); document.write( " $\"D-4%2BD%2BQ=26\"$
\n" ); document.write( "4. $\"2D%2BQ=30\"$
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\n" ); document.write( " $\"5%28D-4%29%2B10D%2B25Q=310\"$
\n" ); document.write( " $\"5D-20%2B10D%2B25Q=310\"$
\n" ); document.write( "5. $\"15D%2B25Q=330\"$
\n" ); document.write( "Multiply eq. 4 by (-25) and add to eq. 5.
\n" ); document.write( " $\"-50D-25Q%2B15D%2B25Q=-750%2B330\"$
\n" ); document.write( " $\"-35D=-420\"$
\n" ); document.write( " $\"highlight%28+D=12%29\"$
\n" ); document.write( "Then,
\n" ); document.write( " $\"N=D-4\"$
\n" ); document.write( " $\"highlight%28+N=8%29\"$
\n" ); document.write( "and finally,
\n" ); document.write( " $\"8%2B12%2BQ=26\"$
\n" ); document.write( " $\"highlight%28+Q=6%29\"$ \n" ); document.write( "

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