document.write( "Question 505724: A coin collector has 31 dimes and nickels with a total face value of $2.40. (They are actually worth a lot more.) How many of each coin does she have? \n" ); document.write( "

Algebra.Com's Answer #339952 by oberobic(2304) $\"\"$ $\"About$

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With money problems you have to keep track of the value of the coins and the number of coins.
\n" ); document.write( "n = number of nickels
\n" ); document.write( "5n = value
\n" ); document.write( "d = number of dimes
\n" ); document.write( "10d = value
\n" ); document.write( ".
\n" ); document.write( "n + d = 31
\n" ); document.write( "so
\n" ); document.write( "n = 31-d
\n" ); document.write( ".
\n" ); document.write( "5n + 10d = 240 cents (which is easier than fooling with decimals)
\n" ); document.write( ".
\n" ); document.write( "substitute n = 31-d
\n" ); document.write( ".
\n" ); document.write( "5(31-d) +10d = 240
\n" ); document.write( "155 -5d +10d = 240
\n" ); document.write( "5d = 240-155
\n" ); document.write( "5d = 85
\n" ); document.write( "d = 17
\n" ); document.write( ".
\n" ); document.write( "n = 31-17
\n" ); document.write( "n = 14
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\n" ); document.write( "Check using the values.
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\n" ); document.write( "5(14) = 70
\n" ); document.write( "10(17) = 170
\n" ); document.write( "70+170 = 240
\n" ); document.write( "Correct.
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\n" ); document.write( "Answer: The collector has 14 nickels and 17 dimes.
\n" ); document.write( ".
\n" ); document.write( "Done. \n" ); document.write( "

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