document.write( "Question 854704: If 2 men and 3 women can complete a task in 8 days; and 4 men and 5 women can complete a task in 12 days then how many women are required to complete a task in a day? \n" ); document.write( "
Algebra.Com's Answer #514914 by Edwin McCravy(20054)\"\" \"About 
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document.write( "If 2 men and 3 women can complete a task in 8 days; and 4 men and 5 women can complete a task in 12 days then \r\n" );
document.write( "Suppose 1 man can complete a task alone in x days.  Then 1 man's working rate is 1 job per x days or \"1_job%2Fx_days\" of \"1%2Fx\" jobs per day\r\n" );
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document.write( "Then 2 men's combined working rate is 2 times \"1%2Fx\" or \"2%2Fx\" jobs per how many women are required to complete a task in a day?\r\n" );
document.write( "day.\r\n" );
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document.write( "Suppose 1 woman can complete a task alone in y days.  Then 1 woman's working rate is 1 job per y days or \"1_job%2Fy_days\" or \"1%2Fy\" jobs per day.\r\n" );
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document.write( "Then 3 women's combined working rate is 3 times \"1%2Fy\" or \"3%2Fy\" jobs per day.\r\n" );
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document.write( ">>2 men and 3 women can complete a task in 8 days<<\r\n" );
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document.write( "Their combined work rate is 1 job per 8 days or \"1_job%2F8_days\" of \"1%2F8\" jobs per day.\r\n" );
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document.write( "The first equation comes from: \r\n" );
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document.write( "\"%28matrix%284%2C1%2C%0D%0A%0D%0A2%2C+%22men%27s%22%2C+work%2Crate%29%29\"\"%22%22%2B%22%22\"\"%28matrix%284%2C1%2C%0D%0A%0D%0A3%2C+%22women%27s%22%2C+work%2Crate%29%29\"\"%22%22=%22%22\"\"%28matrix%284%2C1%2C%0D%0A%0D%0ATheir%2C+combined%2C+work%2Crate%29%29\"\r\n" );
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document.write( "\"2%2Fx\"\"%22%22%2B%22%22\"\"3%2Fy\"\"%22%22=%22%22\"\"1%2F8\"   \r\n" );
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document.write( ">>4 men and 5 women can complete a task in 12 days<<\r\n" );
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document.write( "Exactly the same way, the second equation is\r\n" );
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document.write( "\"4%2Fx\"\"%22%22%2B%22%22\"\"5%2Fy\"\"%22%22=%22%22\"\"1%2F12\"\r\n" );
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document.write( "So we have the system of two equations in two unknowns:\r\n" );
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document.write( "\"system%282%2Fx%2B3%2Fy=1%2F8%2C4%2Fx%2B5%2Fy=1%2F12%29\"\r\n" );
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document.write( "To solve that DO NOT CLEAR OF FRACTINS! Instead use\r\n" );
document.write( "elimination just as they are.  To make the first terms\r\n" );
document.write( "cancel multiply the first equation by -2\r\n" );
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document.write( "\"system%28-4%2Fx-6%2Fy=-2%2F8%2C4%2Fx%2B5%2Fy=1%2F12%29\"\r\n" );
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document.write( "Add the two equations term by term:\r\n" );
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document.write( "\"-1%2Fy=-2%2F8%2B1%2F12\"\r\n" );
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document.write( "\"-1%2Fy=-1%2F4%2B1%2F12\"\r\n" );
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document.write( "\"-1%2Fy=-3%2F12%2B1%2F12\"\r\n" );
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document.write( "\"-1%2Fy=-2%2F12\"\r\n" );
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document.write( "Cross multiply:\r\n" );
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document.write( "\"-2y+=+-12\"\r\n" );
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document.write( "\"y+=+6\"\r\n" );
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document.write( "So 1 woman can complete 1 task in 6 days.\r\n" );
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document.write( ">>how many women are required to complete a task in a day?<<\r\n" );
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document.write( "So 6 women can complete 1 task in 1 day.\r\n" );
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document.write( "Edwin

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