document.write( "Question 1163227: In a class of 52 students 16 are science students. If 1/3 of the boys and 1/4 of the girls assign students, how many boys are in the class? \n" ); document.write( "

Algebra.Com's Answer #787262 by ikleyn(52803) $\"\"$ $\"About$

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\n" ); document.write( "In a class of 52 students 16 are science students.
\n" ); document.write( "If 1/3 of the boys and 1/4 of the girls $\"highlight%28cross%28assign%29%29\"$ are a Science students, how many boys are in the class?
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\n" ); document.write( "\n" ); document.write( " To make an impression (and to shake your mind), I can solve the problem differently.\r
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document.write( "Let x be    of the boys  and  let y be    of the girls in the class.\r\n" );
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document.write( "Then the number of boys is 3x and the number of girls is 4y.\r\n" );
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document.write( "So we have two equations\r\n" );
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document.write( "     x +  y = 16      (1)\r\n" );
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document.write( "    3x + 4y = 52.     (2)\r\n" );
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document.write( "It is equivalent to  (after multiplying the first equation by 3)\r\n" );
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document.write( "    3x + 3y = 48      (3)\r\n" );
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document.write( "    3x + 4y = 52.     (4)\r\n" );
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document.write( "which implies  (subtracting equation (3) from (4) )\r\n" );
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document.write( "          y = 52 - 48 = 4.\r\n" );
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document.write( "Thus the number of girls in the class is 4*4 = 16,  and the boys are the rest population  52 - 16 = 36.\r\n" );
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\n" ); document.write( "\n" ); document.write( "What I did (introduced the unknowns by a non-standard way) may work productively and facilitate solutions in many other cases.\r
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