document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=248513>Question 248513</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A bank contains 30 coins, consisting of nickles, quarters, and dimes.there are twice as many nickles as quarters and the remaining are dimes.if the total value of the coins is $3.35, what is the number of each type of coin in the bank? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #181146 by </B><A HREF=/tutors/aboutme.mpl?userid=oberobic><B>oberobic(2304)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=oberobic><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=181146\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> When you work with coins, you have to keep in mind that there will be counts of the coins and values of the coins to balance.<BR>\n" );
document.write( "n = number of nickels <BR>\n" );
document.write( "5n = the value of the nickels in cents<BR>\n" );
document.write( "d = number of dimes<BR>\n" );
document.write( "10d = value of the dimes in cents<BR>\n" );
document.write( "q = quarters<BR>\n" );
document.write( "25q = value of the quarters in cents<BR>\n" );
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document.write( "We are told the total value:<BR>\n" );
document.write( "5n + 10d + 25q = 335 cents<BR>\n" );
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document.write( "Note that everything needs to be in terms of cents.<BR>\n" );
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document.write( "We are told:<BR>\n" );
document.write( "n + d + q = 30.<BR>\n" );
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document.write( "We also are told:<BR>\n" );
document.write( "n = 2q<BR>\n" );
document.write( ", which means the number of nickels is twice the number of quarters.<BR>\n" );
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document.write( "So we have defined 3 equations and we have 3 unknowns...hmmm...<BR>\n" );
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document.write( "5n + 10d + 25q = 335<BR>\n" );
document.write( "n + d + q = 30<BR>\n" );
document.write( "n = 2q<BR>\n" );
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document.write( "Substituting 2q for n, we have<BR>\n" );
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document.write( "5(2q) + 10d + 25q = 335<BR>\n" );
document.write( "2q + d + q = 30<BR>\n" );
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document.write( "Simplifying, we have<BR>\n" );
document.write( "10q + 10d + 25q = 335<BR>\n" );
document.write( "10d + 35q = 335<BR>\n" );
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document.write( "2q + d + q = 30<BR>\n" );
document.write( "3q + d = 30<BR>\n" );
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document.write( "d = 30 - 3q<BR>\n" );
document.write( ", which seems obvious if you think about it.<BR>\n" );
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document.write( "10(30-3q) + 35q = 335<BR>\n" );
document.write( "300 - 30q + 35q = 335<BR>\n" );
document.write( "5q = 35<BR>\n" );
document.write( "q = 7<BR>\n" );
document.write( ", so we think we have 7 quarters<BR>\n" );
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document.write( "n = 2q <BR>\n" );
document.write( "n = 14 nickels<BR>\n" );
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document.write( "Since there are 30 coins, then there must be 9 dimes.<BR>\n" );
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document.write( "We can check the values to see if they total 335.<BR>\n" );
document.write( "5n + 10d + 25q = 335 cents<BR>\n" );
document.write( "5n = 5(14) = 70 cents<BR>\n" );
document.write( "7q = 7(25) = 175 cents<BR>\n" );
document.write( "9d = 9(10) = 90 cents<BR>\n" );
document.write( "70 + 175 + 90 = 335 cents<BR>\n" );
document.write( "So it checks.<BR>\n" );
document.write( "Done. </SPAN>\n" );
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