document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=172826>Question 172826</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Joe has a collection of nickles and dimes that is worth, $7.05. If the # of dimes were doubled, and the # of nicles were increased by eight, the value of the coins would be, $11.75. How many dimes does he have?\r<BR>\n" );
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document.write( "It really helps me to understand if I can See each step to solve this problem written out like in a math book. Thank you </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #127684 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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/cgi-bin/show-face.mpl?user=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=127684\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d ALIGN=MIDDLE  ALT=\"d\"   DISABLED_style= \"max-width:90%; height:auto;\" > be the number of dimes and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" > be the number of nickels.\r<BR>\n" );
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document.write( "That means that the <b><i>value</i></b> of his dimes is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10d ALIGN=MIDDLE  ALT=\"10d\"   DISABLED_style= \"max-width:90%; height:auto;\" > cents and the <b><i>value</i></b> of his nickels is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5n ALIGN=MIDDLE  ALT=\"5n\"   DISABLED_style= \"max-width:90%; height:auto;\" > cents.\r<BR>\n" );
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document.write( "I expressed those values in terms of cents because it is less messy if you don't have to deal with decimal fractions as coefficients in the equations, but the problem would have worked out just as well to say the value of the dimes is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.10d ALIGN=MIDDLE  ALT=\"0.10d\"   DISABLED_style= \"max-width:90%; height:auto;\" > dollars.  The only thing you have to remember if you express the value in cents is to change the total value numbers, i.e. $7.05 and $11.75 to 705 cents and 1175 cents.\r<BR>\n" );
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document.write( "The first thing we know is that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10d+%2B+5n=705 ALIGN=MIDDLE  ALT=\"10d+%2B+5n=705\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Next, if we double the number of dimes, we now have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2d ALIGN=MIDDLE  ALT=\"2d\"   DISABLED_style= \"max-width:90%; height:auto;\" > dimes, the value of which is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%282d%29=20d ALIGN=MIDDLE  ALT=\"10%282d%29=20d\"   DISABLED_style= \"max-width:90%; height:auto;\" > cents.  If we increase the number of nickels by 8, then the value of the nickels becomes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%28n%2B8%29=5n%2B40 ALIGN=MIDDLE  ALT=\"5%28n%2B8%29=5n%2B40\"   DISABLED_style= \"max-width:90%; height:auto;\" > cents.\r<BR>\n" );
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document.write( "Now we can say <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20d+%2B+5n+%2B+40+=+1175 ALIGN=MIDDLE  ALT=\"20d+%2B+5n+%2B+40+=+1175\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Collect like terms and put it in standard form and you get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20d+%2B+5n+=+1135 ALIGN=MIDDLE  ALT=\"20d+%2B+5n+=+1135\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  \r<BR>\n" );
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document.write( "That gives us a system of two equations in two variables that can be solved by a variety of methods.  I choose to use the elimination method because I can see that the coefficients in the two equations lend themselves to a tidy solution by using elimination.\r<BR>\n" );
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document.write( "Step 1:  Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10d+%2B+5n=705 ALIGN=MIDDLE  ALT=\"10d+%2B+5n=705\"   DISABLED_style= \"max-width:90%; height:auto;\" > 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;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-10d+-+5n+=+-705 ALIGN=MIDDLE  ALT=\"-10d+-+5n+=+-705\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Step 2:  Add the result of Step 1 to the second equation, namely <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20d+%2B+5n+=+1135 ALIGN=MIDDLE  ALT=\"20d+%2B+5n+=+1135\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-10d%2B20d-5n%2B5n=-705%2B1135 ALIGN=MIDDLE  ALT=\"-10d%2B20d-5n%2B5n=-705%2B1135\"   DISABLED_style= \"max-width:90%; height:auto;\" > or, after simplifying, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10d%2B0n=430 ALIGN=MIDDLE  ALT=\"10d%2B0n=430\"   DISABLED_style= \"max-width:90%; height:auto;\" >  (Notice how the coefficient on <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" > went to zero, effectively <b><i>eliminating</i></b> that variable?  Hence the name.)\r<BR>\n" );
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document.write( "Step 3:  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;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10d=430 ALIGN=MIDDLE  ALT=\"10d=430\"   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=d=43 ALIGN=MIDDLE  ALT=\"d=43\"   DISABLED_style= \"max-width:90%; height:auto;\" > telling us that the original number of dimes was 43.\r<BR>\n" );
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document.write( "But you aren't quite done yet, even though you have answered the question.  We need to check our work to make sure we didn't make some silly mistake.\r<BR>\n" );
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document.write( "If the original number of dimes was 43, then there must have been $4.30 in dimes.  $7.05 minus $4.30 is $2.75, meaning that there must have been $2.75 worth of nickels.  Dividing by $0.05 we get 55, telling us there were 55 nickels to begin with.\r<BR>\n" );
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document.write( "If we double the dimes, we get 2 times 43 equals 86 dimes meaning we now have $8.60 worth of dimes, and if we add 8 nickels we get $2.75 plus $0.40 equals $3.15 worth of nickels.\r<BR>\n" );
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document.write( "$8.60 plus $3.15 equals $11.75 which was the amount given in the problem.  Answer checks.  NOW you are done. </SPAN>\n" );
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