document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1044238>Question 1044238</A>: <I><SPAN STYLE=\"word-break: break-all;\"> (2) Owen and Sarah's pre-tax income is $100,000. Suppose that state income tax is 10% of taxable state income and that federal income tax is 10/19 of taxable federal income. Taxable federal income is $100,000 less state income tax. Taxable state income is $100,000 less federal income tax. How much will Owen and Sarah pay in state and federal income tax? Hint: Let TF = taxable federal income and TS = taxable state income. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #659546 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=659546\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> sit = state income tax<BR>\n" );
document.write( "fit = federal income tax<BR>\n" );
document.write( "tsi = taxable state income<BR>\n" );
document.write( "tfi = taxable federal income\r<BR>\n" );
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document.write( "you are given that:\r<BR>\n" );
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document.write( "sit = .10 * (100,000 - fit)<BR>\n" );
document.write( "fit = 10/19 * (100,000 - sit)\r<BR>\n" );
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document.write( "we'll work with sit first.\r<BR>\n" );
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document.write( "sit = .10 * (100,000 - fit)<BR>\n" );
document.write( "fit = 10/19 * (100,000 - sit)\r<BR>\n" );
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document.write( "replace fit with 10/19 * (100,000 - sit) and you get:\r<BR>\n" );
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document.write( "sit = .10 * (100,000 - 10/19 * (100,000 - sit))\r<BR>\n" );
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document.write( "simplify this to get:\r<BR>\n" );
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document.write( "sit = .10 * (100,000 - 10/19 * 100,000 + 10/19 * sit)\r<BR>\n" );
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document.write( "simplify further to get:\r<BR>\n" );
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document.write( "sit = .10 * 100,000 - .10 * 10/19 * 100,000 + .10 * 10/19 * sit\r<BR>\n" );
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document.write( "simplify further to get:\r<BR>\n" );
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document.write( "sit = 10,000 - 1/19 * 100,000 + 1/19 * sit\r<BR>\n" );
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document.write( "simplify further to get:\r<BR>\n" );
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document.write( "sit = 10,000 - 100,000/19 + 1/19 * sit\r<BR>\n" );
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document.write( "subtract 1/19 * sit from both sides of the equation to get:\r<BR>\n" );
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document.write( "sit - 1/19 * sit = 10,000 - 100,000/19\r<BR>\n" );
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document.write( "simplify further to get 18/19 * sit = 190,000/19 - 100,000/19\r<BR>\n" );
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document.write( "simplify further to get 18/19 * sit = 90,000/19\r<BR>\n" );
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document.write( "multiply both sides of this equation by 19/18 to get:\r<BR>\n" );
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document.write( "sit = 19/18 * 90,000/19\r<BR>\n" );
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document.write( "simplify further to get sit = 90,000/18\r<BR>\n" );
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document.write( "simplify further to get sit = 5,000\r<BR>\n" );
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document.write( "you do a similar thing with federal income tax, except now you know what the value of sit is.\r<BR>\n" );
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document.write( "start with:\r<BR>\n" );
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document.write( "fit = 10/19 * (100,000 - sit)\r<BR>\n" );
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document.write( "replace sit with 5,000 to get:\r<BR>\n" );
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document.write( "fit = 10/19 * (100,000 - 5,000)\r<BR>\n" );
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document.write( "simplify to get:\r<BR>\n" );
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document.write( "fit = 10/19 * 95,000\r<BR>\n" );
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document.write( "simplify further to get:\r<BR>\n" );
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document.write( "fit = 50,000\r<BR>\n" );
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document.write( "your solution is:\r<BR>\n" );
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document.write( "federal income tax = 50,000<BR>\n" );
document.write( "state income tax = 5,000\r<BR>\n" );
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document.write( " </SPAN>\n" );
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