document.write( "Question 1206592: Every month. Andie spent 1/5 of his salary on food and 2/3 of the remaining salary on transport. After spending his salary on food and transport, he gave 50% of the rest of the salary to his parents and saved the rest of the $350 How much did he spend on food and transport every month? \n" ); document.write( "
Algebra.Com's Answer #844156 by ikleyn(52776)\"\" \"About 
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\n" ); document.write( "Every month. Andie spent 1/5 of his salary on food and
\n" ); document.write( "2/3 of the remaining salary on transport.
\n" ); document.write( "After spending his salary on food and transport, he gave 50% of the rest of the salary to his parents
\n" ); document.write( "and saved the rest of the $350 How much did he spend on food and transport every month?
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document.write( "Let x be the Andie's total salary.\r\n" );
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document.write( "               Make this table\r\n" );
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document.write( "    (line 1)   1/5 of x is spent on food.        The remainder is R1 = 4/5*x.\r\n" );
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document.write( "    (line 2)   2/3 of R1 is spent on transport.  The remainder is R2 = (1/3)*R1.\r\n" );
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document.write( "    (line 3)   0.5 of R2 is given to parents.    The remaining $350 go to saving.\r\n" );
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document.write( "Let' start analyze from the last line 3.\r\n" );
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document.write( "From the table, from its line 3, the remainder of $350 for saving is the same amount as given to parents.\r\n" );
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document.write( "So, $350 is given to parents.\r\n" );
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document.write( "Thus R2 is twice $350, or $350 + $350 = $700.\r\n" );
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document.write( "Next, from the table, from its line 2,  R2 is 1/3 of R1.\r\n" );
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document.write( "R2 is $700, as we found out in line 3.  Hence,  R1 is 3 * $700 = $2100.\r\n" );
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document.write( "2/3 of R1 is 2/3 * 2100 = $1400.  It is the amount for transport.\r\n" );
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document.write( "Now let's analyze in line 1.\r\n" );
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document.write( "R1 is $2100, as we found out in line 2.\r\n" );
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document.write( "R1 is 4/5 of x.  Hence, x is 5/4*2100 = 2625 dollars and the spending on food is 1/5 * 2625 = 525 dollars.\r\n" );
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document.write( "Thus spending on food and transport together is $1400 + $525 = $1925.    ANSWER\r\n" );
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document.write( "CHECK.  Total salary is $2625.\r\n" );
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document.write( "        1/5 is spent on food,  1/5 * 2625 = 525 dollars. The remainder is R1 = $2625 - $525 = $2100.\r\n" );
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document.write( "        2/3 of R1 is spent on transport.  2/3 of $2100 is $1400,  The remainder R2 = $2100 - $1400 = $700.\r\n" );
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document.write( "        The remainder R2 = $700 is split evenly between parents and saving.  ! correct !\r\n" );
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\n" ); document.write( "\n" ); document.write( "I solved this problem using a backward method.\r
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\n" ); document.write( "\n" ); document.write( "It allows restore unknowns step by step MENTALLY, moving backward
\n" ); document.write( "from the end to the beginning, without using equations.\r
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\n" ); document.write( "\n" ); document.write( "I consciously did not use the method of making and solving equations here,
\n" ); document.write( "since my goal was to make you familiar with this BACKWARD method.\r
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\n" ); document.write( "\n" ); document.write( "It is useful to know and to understand the following fact.\r
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\n" ); document.write( "\n" ); document.write( "If your approach to solving the problem is making and solving equations, then the technical difficulties
\n" ); document.write( "of constructing these equations will quickly increase with increasing the number of subdivisions
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\n" ); document.write( "\n" ); document.write( "But if your approach is a backward method, then it is almost the same, if the length of the chain
\n" ); document.write( "is 5, or 10, or 20. The formal algorithm of the backward method remains the same, with no changes.\r
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\n" ); document.write( "\n" ); document.write( "The backward method remains robust even for long chains of subdivisions (!)\r
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