document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1157837>Question 1157837</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Last month Molly earned $200 a week and got a bonus of $150. During the same period, Harry earned $300 a week and got a bonus of $50. If these earnings continue, when will their earnings be the same, and what will the amount be? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #780765 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=780765\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> i'll keep this simple and assume that there are 4 weeks in a month.<BR>\n" );
document.write( "the actual figure is more like 13/3 weeks in a month.<BR>\n" );
document.write( "this comes out to approximately 4.33 weeks in a month, rounded to 2 decimal places.<BR>\n" );
document.write( "asume 4 weeks in a month for simplicity.\r<BR>\n" );
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document.write( "if you're talking about their earnings being the same in the same number of months, that won't happen.<BR>\n" );
document.write( "if you're talking about their earnings being the same after molly works x months and harry works y months, then you can figure it out.\r<BR>\n" );
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document.write( "you can't however, solve for a specific month.<BR>\n" );
document.write( "the answer will be relative to one of the variable.<BR>\n" );
document.write( "i'll go through it and you'll see what i mean.\r<BR>\n" );
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document.write( "for molly, she earns 200 per week and gets a bonus of 150 at the end of the month.<BR>\n" );
document.write( "her monthly earnings will therefore be 4 * 200 = 800 + 150 = 950<BR>\n" );
document.write( "for harry, he earns 300 per week and gets a bonus of 50 at the end of the month.<BR>\n" );
document.write( "his monthly earnings will therefore be 4 * 300 = 1200 + 50 = 1250.\r<BR>\n" );
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document.write( "you can see that their monthly earnings will never be the same in the same number of months for each.<BR>\n" );
document.write( "harry will always make more than her regardless of the number of months.\r<BR>\n" );
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document.write( "let x equal the number of months molly works and y equal the number of months harry works.<BR>\n" );
document.write( "their earnings will be the same when 950 * x = 1250 * y.<BR>\n" );
document.write( "solve for y to get y = 950 * x / 1250<BR>\n" );
document.write( "this comes out to be y = .76 * x\r<BR>\n" );
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document.write( "what this says is that, if molly works x months, then their total earnings will be the same when harry works .76 * x months.\r<BR>\n" );
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document.write( "if molly works x = 12 months, then their total earnings will be the same when harry works .76 * 12 = 9.12 months.\r<BR>\n" );
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document.write( "molly's total earnings will be 12 * 950 = 11,400<BR>\n" );
document.write( "harry's total earnings will be .76 * 12 * 1250 = 11,400\r<BR>\n" );
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document.write( "this formula will work no matter how many months molly works.\r<BR>\n" );
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document.write( "for example, if molly works 75 months, then their earnings will be the same when harry works .76 * 75 = 57 months.\r<BR>\n" );
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document.write( "molly's total earnings will be 75 * 950 = 71250<BR>\n" );
document.write( "harry's total earnings will be 57 * 1250 = 71250\r<BR>\n" );
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document.write( " </SPAN>\n" );
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