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There are 50 dimes in a roll of dimes, 40 nickels in a roll of nickels, and 40 quarters in a roll of quarters. Robert has a total of 12 rolls of coins with the total value of $70. If he has 3 more rolls of nickels than dimes, how many of each roll of coins does he have?:
\n" ); document.write( ":
\n" ); document.write( "total no. of rolls equation
\n" ); document.write( "n + d + q = 12
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\n" ); document.write( "$Value equation:
\n" ); document.write( ".05(40n) + .10(50d) + .25(40q) = 70
\n" ); document.write( ":
\n" ); document.write( "2n + 5d + 10q = 70
\n" ); document.write( ":
\n" ); document.write( "\"he has 3 more rolls of nickels than dimes,\"
\n" ); document.write( "n = (d+3)
\n" ); document.write( ":
\n" ); document.write( "Replace n with (d+3) in both equations:
\n" ); document.write( "(d+3) = d + q = 12
\n" ); document.write( "2d + q = 12 - 3
\n" ); document.write( "2d + q = 9
\n" ); document.write( "and
\n" ); document.write( "2(d+3) + 5d + 10q = 70
\n" ); document.write( "2d + 6 + 5d + 10q = 70
\n" ); document.write( "7d + 10q = 70 - 6
\n" ); document.write( "7d + 10q = 64
\n" ); document.write( ":
\n" ); document.write( "Two equations, two unknowns, we can handle that, can't we.
\n" ); document.write( "Multiply the 1st two unknown eq by 10, subtract the 2nd one
\n" ); document.write( "20d + 10q = 90
\n" ); document.write( "7d + 10q = 64
\n" ); document.write( "-----------------subtracting eliminates q, find d
\n" ); document.write( "13d + 0q = 26
\n" ); document.write( "d =
\n" ); document.write( "d = 2 rolls of dimes
\n" ); document.write( ":
\n" ); document.write( "See if you can find the no. of rolls of nickels and quarters now.
\n" ); document.write( "Check your solutions in the $value equation.
\n" ); document.write( "If you have difficulty, email me: ankor@dixie-net.com \n" ); document.write( "