document.write( "Question 1208619: When 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 25% of his income after his federal tax was paid. If the accountant's income before taxes amounted to $180000, how much federal tax did he have to pay? \n" ); document.write( "

Algebra.Com's Answer #846991 by ikleyn(52788) $\"\"$ $\"About$

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\n" ); document.write( "When calculating his income tax an accountant realized that his federal tax was 40% of his income after his provincial tax was paid,
\n" ); document.write( "and that his provincial tax was 25% of his income after his federal tax was paid. If the accountant's income before taxes amounted
\n" ); document.write( "to $180000, how much federal tax did he have to pay?
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document.write( "Let F be the federal tax amount, in follars;\r\n" );
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document.write( "let P be the provincial tax, in dollars.\r\n" );
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document.write( "From the problem, we have these two equations\r\n" );
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document.write( "    F = 0.4*(180000 - P),     (1)\r\n" );
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document.write( "    P = 0.25*(180000-F).     (2)\r\n" );
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document.write( "Substitute expression for P from equation (2) into equation (1)\r\n" );
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document.write( "    F = 0.4*(180000-0.25*(180000-F)).     (3)\r\n" );
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document.write( "You have an equation for single unknown F.  Simplify it and find F\r\n" );
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document.write( "    F = 0.4*180000 - 0.4*0.25*(180000-F)\r\n" );
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document.write( "    F = 72000 - 0.1*(180000-F)\r\n" );
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document.write( "    F = 72000 - 18000 + 0.1F\r\n" );
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document.write( "    F - 0.1F = 72000- 18000\r\n" );
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document.write( "       0.9F    =     54000\r\n" );
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document.write( "            F    =      54000/0.9 = 60000.\r\n" );
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document.write( "At this point, the problem is solved completely.\r\n" );
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document.write( "ANSWER.  The federal tax was $60,000.\r\n" );
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