document.write( "Question 73444This question is from textbook algebra 1 CA edition
\n" ); document.write( ": 9)Northern Maywood voted 60% to 40% in favor of a water project. Southern Maywood voted 90% to 10% against the project. The project passed 55% to 45%. If 5900 people voted, how many were from Southern Maywood? The percentages confused me. I didn't know how to set up the equation.
\n" ); document.write( "10) An employer has a daily payroll of $1950 when employing some workers at $120 per day and others at $150 per day. When the number of $120 workers is increased by %50 and the number of $150 workers is decreased 1/5, th new daily payroll is $2400. Find how many workers were originally employed at each rate. \n" ); document.write( "
Algebra.Com's Answer #52583 by Edwin McCravy(20056)\"\" \"About 
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document.write( "9)Northern Maywood voted 60% to 40% in favor \r\n" );
document.write( "of a water project. Southern Maywood voted \r\n" );
document.write( "90% to 10% against the project. The project \r\n" );
document.write( "passed 55% to 45%. If 5900 people voted, how \r\n" );
document.write( "many were from Southern Maywood? The \r\n" );
document.write( "percentages confused me. I didn't know how \r\n" );
document.write( "to set up the equation.\r\n" );
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document.write( "Let S = the total number of voters from S.M\r\n" );
document.write( "Let N = the total number of voters from N.M\r\n" );
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document.write( "Then we can make this table:\r\n" );
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document.write( "          |  S.M. |  N.M.| Totals   \r\n" );
document.write( "------------------------------------------\r\n" );
document.write( "In favor  | .10S  | .60N | .55(5900)\r\n" );
document.write( " Against  | .90S  | .40N | .45(5900)\r\n" );
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document.write( "So the equations are\r\n" );
document.write( " \r\n" );
document.write( ".10S + .60N = 55(5900)\r\n" );
document.write( ".90S + .40N = 45(5900)\r\n" );
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document.write( "Can you solve that system?  If not post\r\n" );
document.write( "again asking how. Be sure to clear of\r\n" );
document.write( "fractions after multiplying out the\r\n" );
document.write( "right sides.\r\n" );
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document.write( "S = 590, N = 5310\r\n" );
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document.write( "The desired answer is 10% of 590, or 59.\r\n" );
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document.write( "To check, fill in the chart with numbers:\r\n" );
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document.write( "          |  S.M. |  N.M.| Totals   \r\n" );
document.write( "------------------------------------------\r\n" );
document.write( "In favor  |   59  | 3186 | 3245\r\n" );
document.write( " Against  |  531  | 2124 | 2655\r\n" );
document.write( "------------------------------------------\r\n" );
document.write( " Totals   |  590  | 5310 | 5900\r\n" );
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document.write( "It checks because \r\n" );
document.write( "55% of 5900 is 3245\r\n" );
document.write( "45% of 5900 is 2655\r\n" );
document.write( "10% of 590 is 59\r\n" );
document.write( "90% of 590 is 531\r\n" );
document.write( "60% of 5310 is 3186\r\n" );
document.write( "40% of 5310 is 2124\r\n" );
document.write( "and the totals come to 5900\r\n" );
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document.write( "---------------------------------------\r\n" );
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document.write( "10) An employer has a daily payroll of \r\n" );
document.write( "$1950 when employing some workers at \r\n" );
document.write( "$120 per day and others at $150 per day. \r\n" );
document.write( "When the number of $120 workers is \r\n" );
document.write( "increased by %50 and the number of $150 \r\n" );
document.write( "workers is decreased 1/5, the new daily \r\n" );
document.write( "payroll is $2400. Find how many workers \r\n" );
document.write( "were originally employed at each rate.\r\n" );
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document.write( "Let x = number of $120 workers originally\r\n" );
document.write( "Let y = number of $150 workers originally\r\n" );
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document.write( "Make this chart:\r\n" );
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document.write( "            | wages of the | wages of the  | Pay-\r\n" );
document.write( "            | $120 workers | $150 workers  | roll  \r\n" );
document.write( "---------------------------------------------------  \r\n" );
document.write( "  Originally|    $120x     |     $150y     | $1950\r\n" );
document.write( "After change|  $120(x+.5x) |  $150(y-1/5y) | $2400\r\n" );
document.write( "\r\n" );
document.write( "The system of equations is\r\n" );
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document.write( "          $120x     +     $150y     = $1950\r\n" );
document.write( "        $120(x+.5x) +  $150(y-1/5y) = $2400\r\n" );
document.write( "       \r\n" );
document.write( "Which simplifies to \r\n" );
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document.write( "                120x + 150y = 1950\r\n" );
document.write( "      120(1.5x) + 150(4/5y) = 2400\r\n" );
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document.write( "which further simplifies to\r\n" );
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document.write( "                120x + 150y = 1950\r\n" );
document.write( "                180x + 120y = 2400\r\n" );
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document.write( "which further simplifies to\r\n" );
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document.write( "                 12x + 15y = 195\r\n" );
document.write( "                 18x + 12y = 240\r\n" );
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document.write( "which further simplifies to\r\n" );
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document.write( "                 4x + 5y = 65\r\n" );
document.write( "                 3x + 2y = 40\r\n" );
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document.write( "Answer x = 10, y = 5.\r\n" );
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document.write( "So there were 10 $120 workers and 5 $150 workers\r\n" );
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document.write( "To check, put numbers in the chart: \r\n" );
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document.write( "            | wages of the | wages of the  | Pay-\r\n" );
document.write( "            | $120 workers | $150 workers  | roll  \r\n" );
document.write( "---------------------------------------------------  \r\n" );
document.write( "  Originally|   $1200      |     $750      | $1950\r\n" );
document.write( "After change|   $1800      |     $600      | $2400\r\n" );
document.write( "\r\n" );
document.write( "It checks.\r\n" );
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document.write( "Edwin

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