document.write( "Question 255460: toni has a collection of dimes & quarters with a face value of $25.30. She has 27 more quarters than dimes. How many of each coin does she have? \n" ); document.write( "

Algebra.Com's Answer #187720 by oberobic(2304) $\"\"$ $\"About$

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With money problems you have to keep track of the count of each type of coin as well as their value.
\n" ); document.write( "d = number of dimes
\n" ); document.write( "10d = value of the dimes in cents
\n" ); document.write( "q = number of quarters
\n" ); document.write( "25q = value of quarters in cents
\n" ); document.write( "$25.30 = 2530 cents (because you need to convert everything to cents)
\n" ); document.write( "10d + 25q = 2530
\n" ); document.write( ".
\n" ); document.write( "We also know she has 27 more quarters than dimes.
\n" ); document.write( "q = d + 27
\n" ); document.write( ".
\n" ); document.write( "Substituting q = d+27 into the total value equation, we have:
\n" ); document.write( "10d + 25(d+27) = 2530
\n" ); document.write( "10d + 25d + 675 = 2530
\n" ); document.write( "35d = 1855
\n" ); document.write( "d = 53
\n" ); document.write( ".
\n" ); document.write( "q = d + 27
\n" ); document.write( "q = 53 + 27
\n" ); document.write( "q = 80
\n" ); document.write( ".
\n" ); document.write( "Check the values
\n" ); document.write( "10d = 530
\n" ); document.write( "25q = 2000
\n" ); document.write( "10d + 25q = 2530
\n" ); document.write( "Checks.
\n" ); document.write( ".
\n" ); document.write( "So she has 53 dimes and 80 quarters.
\n" ); document.write( ".
\n" ); document.write( "Done. \n" ); document.write( "

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