document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=521739>Question 521739</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve this equation: 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? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #346597 by </B><A HREF=/tutors/aboutme.mpl?userid=mamiya><B>mamiya(56)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mamiya><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=346597\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let x be the number of nickels Natalie has, y the number of dimes Dirk has and z the number of quarters Quincy has.\r<BR>\n" );
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document.write( "from the data, we know the number of dimes Dirk has is 5 more than the number of quarters Quincy has, so y= z+5  ...........................(1)<BR>\n" );
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document.write( " if Nathalie gives a nickel to Dirk and receives a quarter from Quincy, Nathalie's money will be 5(x-1) + 25\r<BR>\n" );
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document.write( " if Dirk gives a dime to Quincy and receives a nickel from Nathalie, Dirk's money will be 10(y-1) + 5\r<BR>\n" );
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document.write( " if Quincy gives a quarter to Nathalie and receives a dime from Dirk, Quincy's money will be 25(z-1)+10\r<BR>\n" );
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document.write( "the data said if that happens , they will all have the same amount of money, <BR>\n" );
document.write( " so 5(x-1)+25 = 10(y-1)+5 = 25(z-1)+10  .....................(2)\r<BR>\n" );
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document.write( "from both equations , we got the following  system of equations<BR>\n" );
document.write( "            y=z+5<BR>\n" );
document.write( "            10(y-1)+5= 25(z-1)+10\r<BR>\n" );
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document.write( "        <BR>\n" );
document.write( "         y-z = 5<BR>\n" );
document.write( "         10y-5 = 25z - 15\r<BR>\n" );
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document.write( "        y-z = 5<BR>\n" );
document.write( "        25z-10y = 10\r<BR>\n" );
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document.write( "       y-z = 5<BR>\n" );
document.write( "      5z-2y = 2\r<BR>\n" );
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document.write( "by adding up (2) times the first equation and the second equation, we got<BR>\n" );
document.write( " 2y - 2z + 5z - 2y = 2*5 + 2<BR>\n" );
document.write( "  3z= 12,  so z=4\r<BR>\n" );
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document.write( "  y = z+5= 4+5 = 9<BR>\n" );
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document.write( "from the equation (2), we have 5(x-1)+25= 10(y-1)+5 = 10y - 5<BR>\n" );
document.write( "so, 5x+20= 10y - 5<BR>\n" );
document.write( "     x+4= 2y - 1<BR>\n" );
document.write( "    x= 2y - 1 -4 <BR>\n" );
document.write( "     = 2*9- 5<BR>\n" );
document.write( "     =13<BR>\n" );
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document.write( "     so, originally, Nathalie had 13 coins, Dirk 9 coins and Quincy 4 coins.\r<BR>\n" );
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document.write( "to check: let n be the among of Nathalie's money, d Dirk's and q Quincy's<BR>\n" );
document.write( "n= 13 *5= 65 cents         d= 9*10=90 cents      q=4*25=100 cents<BR>\n" );
document.write( "if Nathalie gives a 5 cents to dirk and receives 25 cents from Quincy, she will have 85 cents.<BR>\n" );
document.write( "if Dirk gives 10 cents to Quincy and receives 5 cents from Nathalie, he will have 85 cents.<BR>\n" );
document.write( "if Quincy gives a quarter to Nathalie and receives a dime from Dirk, He will have 85 cents.\r<BR>\n" );
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document.write( "  \r<BR>\n" );
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document.write( " </SPAN>\n" );
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