document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=437114>Question 437114</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In her purse Anita has 16 coins (nickels,dimes,and quarters), worth $2.05. She has three times as many dimes as 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 #302334 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=302334\">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 of each coin denomination as well as the value. For example, let d=number of dimes.  Then the value of the number of dimes = 10d.  Let n=number of nickels, 5n = value of nickels.  Similarly, q=number of quarters and 25q=value of the quarters.<BR>\n" );
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document.write( "We're told she has nickels, dimes, and quarters worth $2.05 or 205 cents.<BR>\n" );
document.write( "5n + 10d + 25q = 205<BR>\n" );
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document.write( "We're also told she has 16 coins, so<BR>\n" );
document.write( "n + d + q = 16<BR>\n" );
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document.write( "And we're told she has 3 times as many dimes as nickels:<BR>\n" );
document.write( "3n = d<BR>\n" );
document.write( "or<BR>\n" );
document.write( "d = 3n<BR>\n" );
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document.write( "We can use simultaneous equations.<BR>\n" );
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document.write( "5n + 10d + 25q = 205<BR>\n" );
document.write( "Divide by 5<BR>\n" );
document.write( "n + 2d + 5q = 41<BR>\n" );
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document.write( "Substitute d = 3n in the equations<BR>\n" );
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document.write( "n + 2(3n) + 5q = 41<BR>\n" );
document.write( "n + 6n + 5q = 41<BR>\n" );
document.write( "7n + 5q = 41<BR>\n" );
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document.write( "n + 3n + q = 16<BR>\n" );
document.write( "4n + q = 16<BR>\n" );
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document.write( "So we have two equations with two unknowns.<BR>\n" );
document.write( "7n + 5q = 41<BR>\n" );
document.write( "4n + q = 16<BR>\n" );
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document.write( "Multiply the second equation by 5<BR>\n" );
document.write( "20n + 5q = 80<BR>\n" );
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document.write( "7n + 5q = 41<BR>\n" );
document.write( "20n + 5q = 80<BR>\n" );
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document.write( "Subtract the second equation from the first.<BR>\n" );
document.write( "-13n = -39<BR>\n" );
document.write( "n = 3<BR>\n" );
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document.write( "Therefore d = 3n = 9<BR>\n" );
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document.write( "Therefore q = 16 - 3 -9 = 4<BR>\n" );
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document.write( "Our tentative answer is:<BR>\n" );
document.write( "n = 3<BR>\n" );
document.write( "d = 9<BR>\n" );
document.write( "q = 4<BR>\n" );
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document.write( "Always check your answer.  In this case, we have to use the \"value\" equation since we used the \"count\" equation to figure out how many quarters.<BR>\n" );
document.write( "What is the total value?<BR>\n" );
document.write( "3*5 = 15 cents<BR>\n" );
document.write( "9*10 = 90 cents<BR>\n" );
document.write( "4*25 = 100 cents<BR>\n" );
document.write( "45 + 90 + 100 = 205 cents<BR>\n" );
document.write( "Correct.<BR>\n" );
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document.write( "Answer:  She has 3 nickels, 9 dimes, and 4 quarters.<BR>\n" );
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document.write( "Done. </SPAN>\n" );
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