document.write( "Question 1047747: Chocolates were equally distributed in a class of girls. Had there been 20 girls more each would have received one chocolate less. and had there been 20 girls less each would have received 3 chocolates more. find the no of girls in the class and no. of chocolates received by each girl.
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Algebra.Com's Answer #663283 by ikleyn(52832) $\"\"$ $\"About$

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\n" ); document.write( "Chocolates were equally distributed in a class of girls. Had there been 20 girls more each would have received one chocolate less.
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document.write( "Let G = the number of girls in the class and C = the number of chocolates received by each girl.\r\n" );
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document.write( "Then\r\n" );
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document.write( "(G+20)*(C-1) = GC    (1)    (\"Had there been 20 girls more each would have received one chocolate less\")\r\n" );
document.write( "(G-20)*(C+3) = GC    (2)    (\"had there been 20 girls less each would have received 3 chocolates more\")\r\n" );
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document.write( "We have to equations in two unknowns, but the equations are non-linear.\r\n" );
document.write( "Simplify each of the equations. Equation (1) becomes \r\n" );
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document.write( "GC + 20C - G - 20 = GC,  or,  canceling GC in both sides,\r\n" );
document.write( "20C - G - 20 = 0,  or\r\n" );
document.write( "20C - G = 20.         (3)\r\n" );
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document.write( "Equation (2) becomes \r\n" );
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document.write( "GC - 20C +3G - 60 = GC,  or,  canceling GC in both sides,\r\n" );
document.write( "-20C + 3G - 60 = 0,  or\r\n" );
document.write( "-20C + 3G = 60.       (4)\r\n" );
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document.write( "Now we have an equivalent system of two equations (3) and (4) in two unknowns, but this time the equations are linear.\r\n" );
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document.write( "Add the equation (3) and the equation (4) (both sides). You will get\r\n" );
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document.write( "2G = 20 + 60 = 80  --->  G =  = 40. \r\n" );
document.write( "Thus the number of girls in the class is 40.\r\n" );
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document.write( "Then from (3) 20C = G + 20 = 40 + 20 = 60.\r\n" );
document.write( "The number of chocolates each girl received in the basic scenario is  = 3.\r\n" );
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document.write( "Please check this answer on your own.\r\n" );
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document.write( "Answer. 40 girls in the class received 3 chocolates each.\r\n" );
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