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 #543458 by Edwin McCravy(20054)\"\" \"About 
You can put this solution on YOUR website!
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. If Natalie gives Dirk a
\n" ); document.write( "nickel, Dirk gives Quincy a dime, and Quincy gives Natalie a quarter; they
\n" ); document.write( "will all have the same amount of money.
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document.write( "Let's avoid decimals by using cents rather than dollars.\r\n" );
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document.write( "Natalie has N nickels. She has 5N cents\r\n" );
document.write( "Dirk has D dimes. He has 10D cents\r\n" );
document.write( "Quincy has Q quarters.  So he has 25Q cents.\r\n" );
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\n" ); document.write( "Dirk has five more dimes than Quincy has quarters.
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document.write( "So D = Q+5 \r\n" );
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document.write( "So in the beginning, Natalie has 5N, Dirk has 10D, and Quincy has 25Q.\r\n" );
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\n" ); document.write( "...Natalie gives Dirk a nickel,
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document.write( "Natalie now has 5N-5, Dirk now has 10D+5, and Quincy still has 25Q.\r\n" );
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\n" ); document.write( "Dirk gives Quincy a dime,
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document.write( "Natalie still has 5N-5, Dirk now has 10D+5-10, and Quincy now has 25Q+10\r\n" );
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\n" ); document.write( "and Quincy gives Natalie a quarter;
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document.write( "Natalie now has 5N-5+25, Dirk still has 10D+5-10 and Quincy now has 25Q+10-25 \r\n" );
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\n" ); document.write( "they will all have the same amount of money.
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document.write( "Therefore\r\n" );
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document.write( "5N-5+25 = 10D+5-10 = 25Q+10-25\r\n" );
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document.write( "5N+20 = 10D-5 = 25Q-15\r\n" );
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document.write( "Since D = Q+5\r\n" );
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document.write( "5N+20 = 10(Q+5)-5 = 25Q-15\r\n" );
document.write( "         10Q+50-5 = 25Q-15\r\n" );
document.write( "           10Q+45 = 25Q-15\r\n" );
document.write( "               60 = 15Q\r\n" );
document.write( "                4 = Q\r\n" );
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document.write( "Since D = Q+5\r\n" );
document.write( "      D = 4+5\r\n" );
document.write( "      D = 9\r\n" );
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document.write( "5N+20 = 10D-5\r\n" );
document.write( "5N+20 = 10(9)-5\r\n" );
document.write( "5N+20 = 90-5\r\n" );
document.write( "5N+20 = 85\r\n" );
document.write( "   5N = 65\r\n" );
document.write( "    N = 13\r\n" );
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document.write( "Checking (using dollars)\r\n" );
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document.write( "Natalie has 13 nickels or $0.65\r\n" );
document.write( "Dirk has 9 dimes or #0.90\r\n" );
document.write( "Quincy has 4 quarters or $1.00\r\n" );
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\n" ); document.write( "Dirk has five more dimes than Quincy has quarters.
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document.write( "That checks since 9 = 4+5 \r\n" );
document.write( "So in the beginning, Natalie has $0.65, Dirk has $0.90, and Quincy has $1.00.\r\n" );
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\n" ); document.write( "...Natalie gives Dirk a nickel,
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document.write( "Natalie now has $0.60, Dirk now has $0.95, and Quincy still has $1.00.\r\n" );
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\n" ); document.write( "Dirk gives Quincy a dime,
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document.write( "Natalie still has $0.60, Dirk now has $0.85, and Quincy now has $1.10\r\n" );
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\n" ); document.write( "and Quincy gives Natalie a quarter;
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document.write( "Natalie now has $0.85, Dirk still has $0.85 and Quincy now has $0.85 \r\n" );
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\n" ); document.write( "They all have the same amount of money, 85 cents. So the answer is correct.
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document.write( "Edwin
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