document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1200476>Question 1200476</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A piggy bank contains only nickels, dimes, and quarters. If there are 76 coins worth $8.50, and there are twice as many dimes as nickels, how many of each coin are there? <BR>\n" );
document.write( "Show all of your work.\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #834615 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=834615\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Answer: <font color=red>21 nickels, 42 dimes, 13 quarters</font>\r<BR>\n" );
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document.write( "Work Shown:<BR>\n" );
document.write( "n = number of nickels<BR>\n" );
document.write( "d = number of dimes<BR>\n" );
document.write( "q = number of quarters<BR>\n" );
document.write( "n+d+q = 76 coins total<BR>\n" );
document.write( "5n+10d+25q = 850 cents in total value<BR>\n" );
document.write( "d = 2n since there are twice as many dimes as nickels\r<BR>\n" );
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document.write( "Applying substitution and solving for q.<BR>\n" );
document.write( "n+d+q = 76<BR>\n" );
document.write( "n+2n+q = 76 ... plug in d = 2n<BR>\n" );
document.write( "3n+q = 76<BR>\n" );
document.write( "q = 76-3n\r<BR>\n" );
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document.write( "Also,<BR>\n" );
document.write( "5n+10d+25q = 850<BR>\n" );
document.write( "5n+10(2n)+25q = 850 ... plug in d = 2n<BR>\n" );
document.write( "5n+20n+25q = 850<BR>\n" );
document.write( "25n+25q = 850<BR>\n" );
document.write( "25(n+q) = 850<BR>\n" );
document.write( "n+q = 850/25<BR>\n" );
document.write( "n+q = 34<BR>\n" );
document.write( "n+76-3n = 34 ... plug in q = 76-3n; solve for n<BR>\n" );
document.write( "-2n+76 = 34<BR>\n" );
document.write( "-2n = 34-76<BR>\n" );
document.write( "-2n = -42<BR>\n" );
document.write( "n = -42/(-2)<BR>\n" );
document.write( "n = 21\r<BR>\n" );
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document.write( "Use that value to find the others.<BR>\n" );
document.write( "d = 2n = 2*21 = 42<BR>\n" );
document.write( "q = 76-3n = 76-3*21 = 76-63 = 13\r<BR>\n" );
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document.write( "In summary,<BR>\n" );
document.write( "<font color=red>n = 21<BR>\n" );
document.write( "d = 42<BR>\n" );
document.write( "q = 13</font><BR>\n" );
document.write( "to represent the number of nickels, dimes, and quarters respectively.\r<BR>\n" );
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document.write( "Check:<ul><li>Coin count: 21 nickels + 42 dimes + 13 quarters = 21+42+13 = 76 coins total</li><li>Coin value: 21 nickels + 42 dimes + 13 quarters = 21*5 + 42*10 + 13*25 = 850 cents = $8.50 total value</li><li>The number of dimes (42) is double that of the number of nickels (21).</li></ul>The answers have been confirmed.\r<BR>\n" );
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document.write( "Confirmation using WolframAlpha<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"https://www.wolframalpha.com/input?i=n%2Bd%2Bq+%3D+76%2C5n%2B10d%2B25q%3D850%2Cd%3D2n\">https://www.wolframalpha.com/input?i=n%2Bd%2Bq+%3D+76%2C5n%2B10d%2B25q%3D850%2Cd%3D2n</a><BR>\n" );
document.write( "The CAS mode in GeoGebra has a similar solver feature.<BR>\n" );
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