document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=123351>Question 123351</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 7.	Number problems.  Jill has $3.50 in nickels and dimes.  If she has 50 coins, how many of each type of coin does she have?<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 #90536 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=90536\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "Let n= # of nickels, and d= # of dimes\r<BR>\n" );
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document.write( "Since \"Jill has $3.50 in nickels and dimes\", it can be represented as:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.05n%2B0.1d=3.50 ALIGN=MIDDLE  ALT=\"0.05n%2B0.1d=3.50\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=100%280.05n%2B0.1d%29=100%283.50%29 ALIGN=MIDDLE  ALT=\"100%280.05n%2B0.1d%29=100%283.50%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides by 100 to move the decimal on each number 2 times. This will make every number a whole number.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5n%2B10d=350 ALIGN=MIDDLE  ALT=\"5n%2B10d=350\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute and multiply\r<BR>\n" );
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document.write( "So our first equation is: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5n%2B10d=350 ALIGN=MIDDLE  ALT=\"5n%2B10d=350\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "Now since  Jill has 50 coins, this means that we have the second equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%2Bd=50 ALIGN=MIDDLE  ALT=\"n%2Bd=50\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So we have the system \r<BR>\n" );
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document.write( "Now in order to solve this system by using elimination/addition, we need to solve (or isolate) one variable. I'm going to solve for d.\r<BR>\n" );
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document.write( "In order to solve for one variable, we must eliminate the other variable. So if we wanted to solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d ALIGN=MIDDLE  ALT=\"d\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we would have to eliminate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" > (or vice versa).\r<BR>\n" );
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document.write( "So lets eliminate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" >. In order to do that, we need to have both <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" > coefficients that are equal in magnitude but have opposite signs (for instance 2 and -2 are equal in magnitude but have opposite signs). This way they will add to zero. By adding to zero, they can be eliminated.\r<BR>\n" );
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document.write( "So to make the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" > coefficients equal in magnitude but opposite in sign, we need to multiply both <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" > coefficients by some number to get them to an common number. So if we wanted to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" > to some equal number, we could try to get them to the LCM.\r<BR>\n" );
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document.write( "Since the LCM of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we need to multiply both sides of the top equation by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" > and multiply both sides of the bottom equation by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5 ALIGN=MIDDLE  ALT=\"-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > like this:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%285n%2B10d%29=1%28350%29 ALIGN=MIDDLE  ALT=\"1%285n%2B10d%29=1%28350%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Multiply the top equation (both sides) by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5%28n%2Bd%29=-5%2850%29 ALIGN=MIDDLE  ALT=\"-5%28n%2Bd%29=-5%2850%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Multiply the bottom equation (both sides) by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5 ALIGN=MIDDLE  ALT=\"-5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Distribute and multiply\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5n%2B10d=350 ALIGN=MIDDLE  ALT=\"5n%2B10d=350\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5n-5d=-250 ALIGN=MIDDLE  ALT=\"-5n-5d=-250\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now add the equations together. In order to add 2 equations, group like terms and combine them\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285n-5n%29%2B%2810d-5d%29=350-250 ALIGN=MIDDLE  ALT=\"%285n-5n%29%2B%2810d-5d%29=350-250\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Combine like terms and simplify\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cross%285n-5n%29%2B5d=100 ALIGN=MIDDLE  ALT=\"cross%285n-5n%29%2B5d=100\"   DISABLED_style= \"max-width:90%; height:auto;\" > Notice how the n terms cancel out\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5d=100 ALIGN=MIDDLE  ALT=\"5d=100\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=100%2F5 ALIGN=MIDDLE  ALT=\"d=100%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   DISABLED_style= \"max-width:90%; height:auto;\" > to isolate d\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=20 ALIGN=MIDDLE  ALT=\"d=20\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce\r<BR>\n" );
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document.write( "Now plug this answer into the top equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5n%2B10d=350 ALIGN=MIDDLE  ALT=\"5n%2B10d=350\"   DISABLED_style= \"max-width:90%; height:auto;\" > to solve for x\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5n%2B10d=350 ALIGN=MIDDLE  ALT=\"5n%2B10d=350\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the first equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5n%2B10%2820%29=350 ALIGN=MIDDLE  ALT=\"5n%2B10%2820%29=350\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=20 ALIGN=MIDDLE  ALT=\"d=20\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5n=350-200 ALIGN=MIDDLE  ALT=\"5n=350-200\"   DISABLED_style= \"max-width:90%; height:auto;\" >Subtract 200 from both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5n=150 ALIGN=MIDDLE  ALT=\"5n=150\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms on the right side\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=%28150%29%2F%285%29 ALIGN=MIDDLE  ALT=\"n=%28150%29%2F%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by 5 to isolate n\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=30 ALIGN=MIDDLE  ALT=\"n=30\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide\r<BR>\n" );
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document.write( "So our answer is\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=30 ALIGN=MIDDLE  ALT=\"n=30\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=20 ALIGN=MIDDLE  ALT=\"d=20\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "which means that Jill has 30 nickels and 20 dimes </SPAN>\n" );
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