document.write( "Question 1144331: A village has a population of 500 and a play is performed in that village. Men play - 748 rupees, women - 712 rupees and children - 45 rupees to watch the play. The theater company receives a total of Rs. 300,000 (3 lakhs). So what will be the number of men, women and children in that village? \n" ); document.write( "

Algebra.Com's Answer #765411 by ikleyn(52788) $\"\"$ $\"About$

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document.write( "From the condition, you have these two equations\r\n" );
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document.write( "      x +     y +    z =    500    (1)\r\n" );
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document.write( "  748*x + 712*y + 45*z = 300000    (2)\r\n" );
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document.write( "where x is the number of men, y is the number of women and z is the number of children.\r\n" );
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document.write( "From equation (1), express z = 500-x-y  and substitute it into equation (2). You will get\r\n" );
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document.write( "  748*x + 712*y + 45*(500-x-y) = 300000.\r\n" );
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document.write( "Simplify it\r\n" );
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document.write( "  703x  + 667y  = 300000 - 45*500 = 277500.\r\n" );
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document.write( "Now we should find integer solution/solutions to the last equation.\r\n" );
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document.write( "The simplest way is to express y = , put this formula into Excel, run for x= 1, 2, 3, 4, . . . and search for integer y\r\n" );
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document.write( "In this way I got the integer solution  x = 149,   y = 259.\r\n" );
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document.write( "Then z = 500-x-y = 500-149-259 = 92.\r\n" );
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document.write( "ANSWER.  149 men,  259 women and 92 children.\r\n" );
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