document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=438675>Question 438675</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve this equation:<BR>\n" );
document.write( "Betty has $8.60 in nickels, dimes, and quarters. She has 6 fewer quarters than nickels and 3 more dimes than twice the number of nickels. How many of each coin does she have? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #303289 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=303289\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> With coin problems you have to keep track of the counts and the values of the coins.<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( "5n = value of the nickels in cents<BR>\n" );
document.write( "10d = value of the dimes in cents<BR>\n" );
document.write( "25q = value of the quarters in cents<BR>\n" );
document.write( "Note that problem setups that have dollars and cents have to be converted to cents.<BR>\n" );
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document.write( "\"Betty  has $8.60\" is a value statement.<BR>\n" );
document.write( "5n + 10d + 25q = 860 cents<BR>\n" );
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document.write( "She has \"6 fewer quarters than nickels\"<BR>\n" );
document.write( "q = n-6<BR>\n" );
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document.write( "\"3 more dimes than twice the number of nickels\"<BR>\n" );
document.write( "d = 2n + 3<BR>\n" );
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document.write( "Now we can look back at the value equation to see what we can substitute.<BR>\n" );
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document.write( "5n + 10d + 25q = 860<BR>\n" );
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document.write( "Substitute q=n-6 and d= 2n+3, which would make the equation entirely in terms of n.<BR>\n" );
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document.write( "5n + 10(2n+3) + 25(n-6) = 860<BR>\n" );
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document.write( "5n + 20n + 30 + 25n - 150 = 860<BR>\n" );
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document.write( "Collect like terms<BR>\n" );
document.write( "50n - 120 = 860<BR>\n" );
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document.write( "Add 120 to both sides<BR>\n" );
document.write( "50n = 980<BR>\n" );
document.write( "Divide both sides by 50<BR>\n" );
document.write( "n = 19.8<BR>\n" );
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document.write( "This presents us with an unsolvable problem because you cannot have a fractional number of nickels.<BR>\n" );
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document.write( "That having been said, if she were to have had $8.80 instead of $8.60, then we might be able to solve it.<BR>\n" );
document.write( "50n - 120 = 880<BR>\n" );
document.write( "50n = 1000<BR>\n" );
document.write( "n = 20<BR>\n" );
document.write( "d = 2n+3<BR>\n" );
document.write( "d = 43<BR>\n" );
document.write( "q = n-6<BR>\n" );
document.write( "q = 14<BR>\n" );
document.write( "Checking to see if these total $8.80<BR>\n" );
document.write( "5n=5(20) = $1<BR>\n" );
document.write( "10d = 10(43) = $4.30<BR>\n" );
document.write( "25q = 25(14) = $3.50<BR>\n" );
document.write( "$1 + $4.30 + $3.50 = $8.80<BR>\n" );
document.write( "True.<BR>\n" );
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document.write( "But if $8.60 is in the presented problem, then it is unsolvable with \"real\" coins.<BR>\n" );
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document.write( "Done. </SPAN>\n" );
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