document.write( "Question 896368: Coin question
\n" ); document.write( "Natalie has some nickels, Dirk has some dimes and Quincy has some quarters. Dirk has five more dimes than Quincy has quarters. If Natalie gives Dirk a nickel, Dirk gives Quincy a dime, and Quincy gives Natalie a quarter; they will all have the same amount of money. How many coins did each have originally?
\n" ); document.write( "I set up an equation to show how much money Dirk has: .10d + .05 - .10 where d is the number of dimes. For Quincy: .25q + .10 - .25 where q is the number of quarters. I also set up 5 + d = q to show that Dirk has 5 more coins than Quincy then I solved for d (d = q - 5) and substituted that in Dirks formula, but this isn't working. I know intuitively that they each end up with $.85 and that means Natalie has 13 coins, Dirk has 9 and Quincy has 4 at the beginning, but I can't figure out how to write this as an equation. I appreciate the help, Judy \n" ); document.write( "
Algebra.Com's Answer #543456 by ankor@dixie-net.com(22740)\"\" \"About 
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Natalie has some nickels, Dirk has some dimes and Quincy has some quarters.
\n" ); document.write( " Dirk has five more dimes than Quincy has quarters.
\n" ); document.write( "d = q + 5
\n" ); document.write( "If Natalie gives Dirk a nickel, Dirk gives Quincy a dime, and Quincy gives Natalie a quarter; they will all have the same amount of money.
\n" ); document.write( ".10d + .05 - .10 = .25q +.10 - .25
\n" ); document.write( ".10d -.05 = .25q - .15
\n" ); document.write( ".10d = .25q -.15 + .05
\n" ); document.write( ".10d = .25q - .10
\n" ); document.write( "multiply by 10
\n" ); document.write( "d = 2.5q - 1
\n" ); document.write( "we know that d = q + 5
\n" ); document.write( "q + 5 = 2.5q - 1
\n" ); document.write( "5 + 1 = 2.5q - q
\n" ); document.write( "6 = 1.5q
\n" ); document.write( "q = 6/1.5
\n" ); document.write( "q = 4 quarters
\n" ); document.write( "then
\n" ); document.write( "d = 4 + 5 = 9 dimes
\n" ); document.write( ":
\n" ); document.write( "Find n:
\n" ); document.write( ".05n -.05 + .25 = .05n + .20
\n" ); document.write( "we know that
\n" ); document.write( ".05n + .20 = .25q -.15
\n" ); document.write( "Replace q with 4
\n" ); document.write( ".05n + .20 = 1.0 - .15
\n" ); document.write( ".05n = .85 - .20
\n" ); document.write( ".05n = .65
\n" ); document.write( "n = .65/.05
\n" ); document.write( "n = 13 nickels \r
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\n" ); document.write( "\n" ); document.write( " How many coins did each have originally? \n" ); document.write( "
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