document.write( "Question 1201935: For positive numbers a, b, and c, if 2ab = 1, 3bc = 2, and 4ca = 3, what is the value of a + b + c ?\r
\n" ); document.write( "\n" ); document.write( "(A) 29/12
\n" ); document.write( "(B) 9/4
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\n" ); document.write( "(E) 7/4 \n" ); document.write( "

Algebra.Com's Answer #836518 by ikleyn(52788) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "For positive numbers a, b, and c, if 2ab = 1, 3bc = 2, and 4ca = 3, what is the value of a + b + c ?
\n" ); document.write( "(A) 29/12
\n" ); document.write( "(B) 9/4
\n" ); document.write( "(C) 25/12
\n" ); document.write( "(D) 23/12
\n" ); document.write( "(E) 7/4
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\n" ); document.write( "\n" ); document.write( "        The solution by @math_tutor is correct, but can make you shudder.\r
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\n" ); document.write( "\n" ); document.write( "        I will show you an elegant, simple and fine STANDARD solution to this \r
\n" ); document.write( "\n" ); document.write( "        and similar problems, which will make you more than happy.\r
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document.write( "From the given info, we have these equations\r\n" );
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document.write( "    ab =      (1)\r\n" );
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document.write( "    bc =      (2)\r\n" );
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document.write( "    ac =      (3)\r\n" );
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document.write( "Multiply all these three equations (their left sides and their right sides separately).  You will get\r\n" );
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document.write( "    a^2*b^2*c^2 =  = ,\r\n" );
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document.write( "or\r\n" );
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document.write( "    (a*b*c)^2 = .\r\n" );
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document.write( "Take the square root of both sides.  Since \"a\", \"b\", and \"c\" are positive, it gives you\r\n" );
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document.write( "    a*b*c = .   (4)\r\n" );
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document.write( "At this point, you may find \"a\", \"b\" and \"c\" separately.\r\n" );
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document.write( "    To find \"a\", divide (4) by (2);\r\n" );
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document.write( "    To find \"b\", divide (4) by (3);\r\n" );
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document.write( "    To find \"c\", divide (4) by (1).\r\n" );
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document.write( "You will get  a =  = ;  b =  = ;  c =  = 1.\r\n" );
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document.write( "Now a + b + c =  +  + 1 =  +  +  =  +  = .    ANSWER\r\n" );
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\n" ); document.write( "\n" ); document.write( "Memorize this method and use it for other similar problems.\r
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