document.write( "Question 1197386: hen calculating his income tax an accountant realized that his federal tax was 40% of his income after his provincial tax was paid, and that his provincial tax was 20% of his income after his federal tax was paid. If the accountant's income before taxes amounted to $46 000, how much federal tax did he have to pay? \n" ); document.write( "

Algebra.Com's Answer #830630 by ikleyn(52778) $\"\"$ $\"About$

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\n" ); document.write( "When calculating his income tax, an accountant realized that his federal tax was 40%
\n" ); document.write( "of his income after his provincial tax was paid, and that his provincial tax was 20%
\n" ); document.write( "of his income after his federal tax was paid.
\n" ); document.write( "If the accountant's income before taxes amounted to $46 000, how much federal tax did he have to pay?
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document.write( "Let F be the federal tax;  P be the provincial tax.\r\n" );
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document.write( "[1]  First sentence is \"his federal tax was 40% of his income after his provincial tax was paid\".\r\n" );
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document.write( "     It means that   F = 0.4*(46000-P).     (1)\r\n" );
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document.write( "[2]  Second sentence is \"his provincial tax was 20% of his income after his federal tax was paid\".\r\n" );
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document.write( "     It means that   P = 0.2*(46000-F).     (2)\r\n" );
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document.write( "[3]  Thus we have two equations for two unknown, so the problem is solvable.\r\n" );
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document.write( "     Since they ask about F, I substitute P from equation (2) into equation (1). I get\r\n" );
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document.write( "         F = 0.4*(46000 - 0.2*(46000-F).\r\n" );
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document.write( "     Simplify and find F\r\n" );
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document.write( "         F = 0.4*46000 - 0.4*0.2*46000 + 0.4*0.2*F\r\n" );
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document.write( "         F - 0.4*0.2F = 0.4*46000 - 0.4*0.2*46000\r\n" );
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document.write( "            0.92F     =  14720\r\n" );
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document.write( "                F     =  14720/0.92 = 16000.\r\n" );
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document.write( "ANSWER.  Federal tax was 16000.\r\n" );
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