document.write( "Question 1175375: Can I have a detailed answer with explanations to the steps for the following question “ In a school, all of the students study physics or chemistry. Sixty percent of the students who study physics also study chemistry, but only one third of the chemistry students study physics. If there are 110 students in this school, how many of them study both of these subjects?” \n" ); document.write( "

Algebra.Com's Answer #800990 by ikleyn(52810) $\"\"$ $\"About$

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\n" ); document.write( "Can I have a detailed answer with explanations to the steps for the following question “
\n" ); document.write( "In a school, all of the students study physics or chemistry.
\n" ); document.write( "Sixty percent of the students who study physics also study chemistry,
\n" ); document.write( "but only one third of the chemistry students study physics.
\n" ); document.write( "If there are 110 students in this school, how many of them study both of these subjects?”
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\n" ); document.write( "\n" ); document.write( " It is a nice problem, and I will show you how to setup it.\r
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\n" ); document.write( "\n" ); document.write( " I am sure that you NEVER saw this way to setup and will be fascinated.\r
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document.write( "The figure below shows all the class, from A to D.\r\n" );
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document.write( "        P h y s i c s  (from  A  to  C)\r\n" );
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document.write( "     |---------------|------------------------|---------------------|\r\n" );
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document.write( "     A               B                        C                     D\r\n" );
document.write( "                        Both (from B to C)\r\n" );
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document.write( "                           C h e m i s t r y  (from  B  to  D)\r\n" );
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document.write( "Part of the class (from A to C) learns Physics.\r\n" );
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document.write( "Part of the class (from B to D) learns Chemistry.\r\n" );
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document.write( "Those in the intersection, from B to C, learn BOTH.\r\n" );
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document.write( "Let x be the unknown number of those, who learn BOTH.\r\n" );
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document.write( "Let P be the number of those who learn Physics and C be the number of those who learn Chemistry.\r\n" );
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document.write( "The problem says that  0.6P = x;  hence, the number of those who learn Physics only is 0.4P.\r\n" );
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document.write( "    Since 0.6P = x,  it implies that 0.4P =  = .\r\n" );
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document.write( "Next, the problem says that   = x;  hence, the number of those who learn Chemistry only is .\r\n" );
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document.write( "    Since  = x,  it implies that  = 2x.\r\n" );
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document.write( "So, the parts are  AB = ;  BC = x;  and  CD = 2x.\r\n" );
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document.write( "Altogether, these 3 parts comprise 110 students.\r\n" );
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document.write( "It means that   + x + 2x = 110.\r\n" );
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document.write( "At this point, the setup is done (!)\r\n" );
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document.write( "To solve this equation and to find x, multiply both sides by 3\r\n" );
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document.write( "    2x + 3x + 6x = 330\r\n" );
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document.write( "        11x      = 330\r\n" );
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document.write( "          x      = 330/11 = 30.\r\n" );
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document.write( "ANSWER.  30 students study both subjects.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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\n" ); document.write( "\n" ); document.write( "Isn't it amazing and beautiful ?\r
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\n" ); document.write( "\n" ); document.write( "You may post me your comments, including your \"THANKS\" for brilliantly presented solution (!)\r
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