document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1165001>Question 1165001</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In a certain state, the first $2500 of SMith's income is not taxed; on the next $5000 of income, the tax is 2%; on all income over $7500, the tax is 5%. If Smith pays a tax of $365, find his income. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #789515 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=789515\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> first 2500 of income is not taxed.<BR>\n" );
document.write( "next 5000 of income is taxed at 2%<BR>\n" );
document.write( "all income over 7500 is taxed at 5%.\r<BR>\n" );
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document.write( "total tax is 365.\r<BR>\n" );
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document.write( "let x = amount of money taxed at 0%.<BR>\n" );
document.write( "let y = amount of money taxed at 2%.<BR>\n" );
document.write( "let z = amount of money taxed at 5%.\r<BR>\n" );
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document.write( "your equation becomes 0 * x + .02 * y + .05 * z = 365\r<BR>\n" );
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document.write( "since you are paying more than 0 tax, then x = 2500.\r<BR>\n" );
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document.write( "since .02 * 5000 = 100, and you still have more taxes to pay, then y = 5000\r<BR>\n" );
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document.write( "since the total tax is 365 and you paid 100 already, then you still owe 265 in taxes.\r<BR>\n" );
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document.write( "this will be at the 5% rate.\r<BR>\n" );
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document.write( "to find out what the income is you set up the equation of .05 * z = 265<BR>\n" );
document.write( "solve for z to get z = 265 / .05 = 5300.\r<BR>\n" );
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document.write( "you have x = 2500, y = 5000, and z = 5300.\r<BR>\n" );
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document.write( "your total income is 2500 + 5000 + 5300 = 12,800.\r<BR>\n" );
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document.write( "the first 2500 of this is not taxed, so the remainder is 12,800 - 2500 = 10,300 with tax on the 2500 = 0.\r<BR>\n" );
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document.write( "the next 5000 of this is taxed at 2%, so the remainder is 10300 - 5000 = 5300 with tax on the 5000 = 100.\r<BR>\n" );
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document.write( "the last 5300 of this is taxed at 5%, so the tax is .05 * 5300 = 265.\r<BR>\n" );
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document.write( "total tax is 0 + 100 + 265 = 365.\r<BR>\n" );
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document.write( "this confirms the solution is correct.\r<BR>\n" );
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document.write( "your solution is that his income is 12,800.\r<BR>\n" );
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