document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=304126>Question 304126</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please Help! I have no idea where to start.\r<BR>\n" );
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document.write( "A company has an income of $100,000<BR>\n" );
document.write( "before paying taxes and a bonus. The bonus B is to be<BR>\n" );
document.write( "20% of the income after deducting income taxes T but<BR>\n" );
document.write( "before deducting the bonus. So<BR>\n" );
document.write( "B = 0.20(100,000 - T ).<BR>\n" );
document.write( "Because the bonus is a deductible expense, the amount of<BR>\n" );
document.write( "income tax T at a 40% rate is 40% of the income after<BR>\n" );
document.write( "deducting the bonus. So<BR>\n" );
document.write( "T = 0.40(100,000 - B).<BR>\n" );
document.write( "a) Use the accompanying graph to estimate the values of<BR>\n" );
document.write( "T and B that satisfy both equations.<BR>\n" );
document.write( "b) Solve the system algebraically to find the bonus and<BR>\n" );
document.write( "the amount of tax. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #217875 by </B><A HREF=/tutors/aboutme.mpl?userid=dabanfield><B>dabanfield(803)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=dabanfield><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=217875\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1.) B = 0.20(100,000 - T )<BR>\n" );
document.write( "2.) T = 0.40(100,000 - B)\r<BR>\n" );
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document.write( "You have two equations in two unknowns to solve simultaneously.\r<BR>\n" );
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document.write( "Rewrite 1.) as\r<BR>\n" );
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document.write( "3.) B = 20000 - .2*T \r<BR>\n" );
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document.write( "and 2.) as\r<BR>\n" );
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document.write( "4.) T = 40000 - .4*B\r<BR>\n" );
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document.write( "Substitute (20000 - .2*T) from 3.) in 4.) and solve for T:\r<BR>\n" );
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document.write( "T = 40000 - .4*(20000 - .2*T)<BR>\n" );
document.write( "T = 40000 - 8000 + .08*T<BR>\n" );
document.write( "T - .08*T = 32000<BR>\n" );
document.write( ".92*T = 3200<BR>\n" );
document.write( "T = 3200/.92\r<BR>\n" );
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document.write( "T = ?\r<BR>\n" );
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document.write( "Take the value for T above and substitute in 3.) to calculate B.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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