document.write( "Question 519701: a collection of nickels and quarters has a total value of $6.40. If there are forty coins in the collection, how many are there of each kind? \n" ); document.write( "

Algebra.Com's Answer #345732 by oberobic(2304) $\"\"$ $\"About$

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With coin problems you have to keep track of the number of coins and their values separately.
\n" ); document.write( "n = number of nickels
\n" ); document.write( "5n = value of the nickels in cents
\n" ); document.write( "q = number of quarters
\n" ); document.write( "25q = value of the quarters in cents
\n" ); document.write( ".
\n" ); document.write( "n+q = 40
\n" ); document.write( "n = 40-q
\n" ); document.write( ".
\n" ); document.write( "5n + 25q = 640 cents
\n" ); document.write( ".
\n" ); document.write( "substitute
\n" ); document.write( ".
\n" ); document.write( "5(40-q) +25q = 640
\n" ); document.write( "200 -5q +25q = 640
\n" ); document.write( "20q = 440
\n" ); document.write( "q = 22
\n" ); document.write( ".
\n" ); document.write( "n = 40-22
\n" ); document.write( "n = 18
\n" ); document.write( ".
\n" ); document.write( "check the values to be sure this is the correct answer
\n" ); document.write( ".
\n" ); document.write( "25(22) = 550 cents
\n" ); document.write( "5(18) = 90 cents
\n" ); document.write( "550 + 90 = 640 cents = $6.40
\n" ); document.write( "correct
\n" ); document.write( ".
\n" ); document.write( "Answer: There are 22 quarters and 18 nickels.
\n" ); document.write( ".
\n" ); document.write( "Done. \n" ); document.write( "

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