document.write( "Question 1172554: If 8 boys went to the washroom, there would be 2/3 as many boys as girls in the room. If 8 girls went to the washroom, there would be 2 times as many boys as girls. How many boys and how many girls are in the class? \n" ); document.write( "

Algebra.Com's Answer #797624 by math_helper(2461) $\"\"$ $\"About$

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document.write( "b = number of boys
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document.write( "g = number of girls\r
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document.write( "b-8 = (2/3)g   (1)
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document.write( "2(g-8) = b     (2)\r
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document.write( "Substitute LHS of (2) for 'b' in (1):
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document.write( "2(g-8)-8 = (2/3)g
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document.write( "2g-24 = (2/3)g
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document.write( "6g-72 = 2g
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document.write( "   4g = 72  
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document.write( "    g = 18  -->(using (1) or (2))-->  b = 20\r
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document.write( "There are 20 boys and 18 girls in the class\r
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document.write( "Check:  
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document.write( "20 - 8 = 12 and 12 = (2/3)18   ((1) checks out)
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document.write( "2(18-8) = 2(10) = 20 = b       ((2) checks out)\r
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