document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=235464>Question 235464</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Employee A and Employee B paychecks totaled $2,388.90.  Employee A worked two hours and Employee B worked 43 hours during this time period.  What is each of their hourly rate?  (There hourly rates may (probably will) be different.)\r<BR>\n" );
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document.write( "A + B = $2,388.90 \r<BR>\n" );
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document.write( "A/2 + B/43 = $2,388.90\r<BR>\n" );
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document.write( "This is what I think the two problems are supposed to be, but when I solve one for A to substitute in the other, it isn't working.  HELP!! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #173429 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=173429\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Garamond\" size=\"+2\">\r<BR>\n" );
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document.write( "Since you said <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE A\ +\ B\ =\ 2388.9\">, you must mean that <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE A\"> represents the amount of A's paycheck and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE B\"> represents the amount of B's paycheck.  That is certainly a reasonable start.\r<BR>\n" );
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document.write( "But if <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE A\"> represents A's paycheck, then <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{A}{2}\"> must represent what A earns in 1 hour, or the hourly rate for A.  Likewise, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{B}{43}\"> must be the hourly rate for B.  Certainly what each of them make in 1 hour cannot add up to the same amount that they both earn in a total of 45 hours.  Hence your second equation is faulty because you don't know the constant amount, that is you have actually introduced a third variable, call it the sum of the rates, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE s\">.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{A}{2}\ +\ \frac{B}{43}\ =\ s\">\r<BR>\n" );
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document.write( "Now what do we do?  Not much, I'm afraid.  Without additional information, you are stuck.\r<BR>\n" );
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document.write( "I started the problem from a different direction.  I let <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large a\"> represent the hourly rate earned by A, and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large b\"> represent B's hourly rate.  That way I could say that <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 2a\"> was the amount of A's paycheck and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 43b\"> was the amount of B's paycheck, and finally, the sum is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 2a\ +\ 43b\ =\ 2388.9\">\r<BR>\n" );
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document.write( "But then I am also stuck for any other information that gives me a different relationship between <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large a\"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large b\">.\r<BR>\n" );
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document.write( "The only thing that you can do is to graph the linear relationship and find the intercepts so that you can say:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 0\ \leq\ a\ \leq\ 1194.45\">\r<BR>\n" );
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document.write( "and then once <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large a\"> is chosen, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large b\"> can be calculated but will be in the range:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 0\ \leq\ b\ <\ 55.56\">\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
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