document.write( "Question 1204269: When calculating his income tax an accountant realized that his federal tax was 25% of his income after his provincial tax was paid, and that his provincial tax was 15% of his income after his federal tax was paid. If the accountant's income before taxes amounted to $120 000, how much federal tax did he have to pay (to the nearest penny)? \n" ); document.write( "

Algebra.Com's Answer #840411 by ikleyn(52790) $\"\"$ $\"About$

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\n" ); document.write( "When calculating his income tax an accountant realized that his federal tax was 25%
\n" ); document.write( "of his income after his provincial tax was paid, and that his provincial tax was 15%
\n" ); document.write( "of his income after his federal tax was paid. If the accountant's income before taxes
\n" ); document.write( "amounted to $120 000, how much federal tax did he have to pay (to the nearest penny)?
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document.write( "Let F be the federal tax amount;\r\n" );
document.write( "let P be the provincial tax amount.\r\n" );
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document.write( "Write equations as you read the problem\r\n" );
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document.write( "    F = 0.25*(120000 - P)      (1)   \"federal tax was 25% of his income after his provincial tax was paid\"\r\n" );
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document.write( "    P = 0.15*(120000 - F)      (2)   \"provincial tax was 15% of his income after his federal tax was paid\"\r\n" );
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document.write( "This system is ready to be solved by substitution - so, substitute P from equation (2) into equation (1).\r\n" );
document.write( "You will get then\r\n" );
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document.write( "    F = 0.25*120000 - 0.25*0.15*(120000-F).\r\n" );
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document.write( "Simplify and find F\r\n" );
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document.write( "    F = 30000 - 0.0375*120000 + 0.0375*F\r\n" );
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document.write( "    F - 0.0375F = 30000 - 0.0375*120000\r\n" );
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document.write( "      0.9625F   =     25500\r\n" );
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document.write( "           F   =     25500/0.9625 = 26493.51  (to the nearest cent)\r\n" );
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document.write( "           P = 0.15*(120000 - 26493.51) = 14025.97  (to the nearest cent)\r\n" );
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document.write( "ANSWER.  Federal tax is  26493.51.   Provincial tax is  14025.97.\r\n" );
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