document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=19754>Question 19754</A>: <I><SPAN STYLE=\"word-break: break-all;\"> ms. lynch has 21 coins in nickle and dimes.Their total value is $1.65.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 #9548 by </B><A HREF=/tutors/aboutme.mpl?userid=mmm4444bot><B>mmm4444bot(95)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mmm4444bot><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=9548\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Hello There:\r<BR>\n" );
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document.write( "Start by assigning variable names for the two unknown amounts that we are asked to find.\r<BR>\n" );
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document.write( "x = number of nickels\r<BR>\n" );
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document.write( "y = number of dimes\r<BR>\n" );
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document.write( "Each nickel is worth $0.05 and each dime is worth $0.10, so we can write an equation because we're told that their total is $1.65.\r<BR>\n" );
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document.write( "0.05*x + 0.10*y = 1.65\r<BR>\n" );
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document.write( "(The asterisks mean multiplication.)\r<BR>\n" );
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document.write( "We're also told that:\r<BR>\n" );
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document.write( "x + y = 21\r<BR>\n" );
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document.write( "If you don't like working with the decimal numbers in the first equation, then multiply both sides by 100 to get whole numbers.\r<BR>\n" );
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document.write( "5*x + 10*y = 165\r<BR>\n" );
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document.write( "x + y = 21\r<BR>\n" );
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document.write( "This is a system of two equations with two variables.  Off the top of my head, I can think of at least five different ways to solve this system.  You didn't ask any questions or tell us what method to use, so I'll just guess.\r<BR>\n" );
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document.write( "I'm going to show you the \"substitution\" method.  The strategy is to solve one of the equations for x, and then substitute the resulting expression for x in the other equation.  This results in an equation with only one variable (for which we can solve easily).\r<BR>\n" );
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document.write( "I'll solve the second equation for x by subtracting y from both sides:\r<BR>\n" );
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document.write( "x = 21 - y\r<BR>\n" );
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document.write( "Now that we know 21 - y is the same as x, we substitute it for x in the first equation:\r<BR>\n" );
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document.write( "5*x + 10*y = 165\r<BR>\n" );
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document.write( "5*(21 - y) + 10*y = 165\r<BR>\n" );
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document.write( "105 - 5*y + 10*y = 165\r<BR>\n" );
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document.write( "5*y = 60\r<BR>\n" );
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document.write( "y = 12\r<BR>\n" );
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document.write( "Now that we know the value of y, we can find the value of x from our equation above:\r<BR>\n" );
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document.write( "x = 21 - y\r<BR>\n" );
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document.write( "x = 21 - 12\r<BR>\n" );
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document.write( "x = 9\r<BR>\n" );
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document.write( "Ms. Lynch has 9 nickels and 12 dimes.  Let's check our result.\r<BR>\n" );
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document.write( "Is 9 + 12 equal to 21 coins?  Yes, it is.\r<BR>\n" );
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document.write( "9 nickels is $0.45, and 12 dimes is $1.20.  Do these amounts add up to $1.65?  Yes, they do.  Our answer is correct.\r<BR>\n" );
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document.write( "~ Mark<BR>\n" );
document.write( " </SPAN>\n" );
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