document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=69850>Question 69850</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am having a hard time figuring out how to write the equation for this problem:\r<BR>\n" );
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document.write( "Joyce makes $6000 more per year than her husband does. Joyce saves 10% of her income for retirement and her husband saves 6%. If altogether they save $5400 per year, then how much does each of them earn per year? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #49769 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=49769\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Joyce makes $6000 more per year than her husband does. Joyce saves 10% of her income for retirement and her husband saves 6%. If altogether they save $5400 per year, then how much does each of them earn per year?\r<BR>\n" );
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document.write( "Suppose we let H represent the amount that her husband earns in a year and J represent the<BR>\n" );
document.write( "amount that Joyce earns.\r<BR>\n" );
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document.write( "The first sentence tells you that J is $6000 more than H.  So if we take away $6000 from<BR>\n" );
document.write( "J the amount left should be H.  In equation form this is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=J+-+%246000+=+H ALIGN=MIDDLE  ALT=\"J+-+%246000+=+H\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "For later convenience, let's rearrange that by first adding $6000 to both sides and then<BR>\n" );
document.write( "subtracting H from both sides to get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=J+-+H+=+%246000 ALIGN=MIDDLE  ALT=\"J+-+H+=+%246000\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now let's look at the second part of the information given in the problem.\r<BR>\n" );
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document.write( "Joyce saves 10% of her income.  That is she saves 10% of J or in decimal form she saves<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.1J ALIGN=MIDDLE  ALT=\"0.1J\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Her husband saves 6% of his income or in decimal form he saves <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.06H ALIGN=MIDDLE  ALT=\"0.06H\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Added together, these two amounts of savings totals $5400.  In equation form this becomes:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.1J+%2B+0.06H+=+%245400 ALIGN=MIDDLE  ALT=\"0.1J+%2B+0.06H+=+%245400\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "You now have 2 linear equations that can be solved simultaneously:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=J+-+H+=+%246000 ALIGN=MIDDLE  ALT=\"J+-+H+=+%246000\"   DISABLED_style= \"max-width:90%; height:auto;\" > and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.1J+%2B+0.06H+=+%245400 ALIGN=MIDDLE  ALT=\"0.1J+%2B+0.06H+=+%245400\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "One way to do it is to multiply the entire bottom equation by -10 so that it becomes:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-J+-+0.6H+=+-%2454000 ALIGN=MIDDLE  ALT=\"-J+-+0.6H+=+-%2454000\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "If you add this equation to the first equation, the J and the -J cancel and the resulting<BR>\n" );
document.write( "equation becomes:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-1.6H+=+-%2448000 ALIGN=MIDDLE  ALT=\"+-1.6H+=+-%2448000\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Calculator time.  Divide both sides by -1.6 to get \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+H+=+%2430000 ALIGN=MIDDLE  ALT=\"+H+=+%2430000\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "And since Joyce makes $6000 more than that, you know she makes:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=J+=+%2436000 ALIGN=MIDDLE  ALT=\"J+=+%2436000\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Check by seeing if 10% of Joyce's salary plus 6% of her husband's salary adds up to be $5400.\r<BR>\n" );
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document.write( "Hope this helps you to see that problems of this sort require 2 equations to solve, and<BR>\n" );
document.write( "that they must be solved as simultaneous linear equations. </SPAN>\n" );
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