document.write( "Question 1186042: Some sweets were distributed equally among 24 children. Then 8 of
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Algebra.Com's Answer #816915 by ikleyn(52835)\"\" \"About 
You can put this solution on YOUR website!
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\n" ); document.write( "Some sweets were distributed equally among 24 children. Then 8 of
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\n" ); document.write( "than before. How many sweets were there in total?
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document.write( "Let n be the total number of sweets (the unknown value under the problem's question).\r\n" );
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document.write( "Notice that the number of children giving away is 8;\r\n" );
document.write( "            the number of children receiving sweets is  24-8 = 16.\r\n" );
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document.write( "The number of sweets each child had at the beginning is  \"n%2F24\".\r\n" );
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document.write( "The number of sweets that 8 children gave to the rest of children was  \"8%2A%282%2F3%29%2A%28n%2F24%29\".\r\n" );
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document.write( "Now 16 children have, in total,  \"16%2A%28n%2F24%29\" + \"8%2A%282%2F3%29%2A%28n%2F24%29\" sweets.\r\n" );
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document.write( "The increment of sweets for each of 16 children is  \"%288%2F16%29%2A%282%2F3%29%2A%28n%2F24%29\" = \"%281%2F2%29%2A%282%2F3%29%2A%28n%2F24%29\".\r\n" );
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document.write( "This increment is equal to 13\r\n" );
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document.write( "      \"%281%2F2%29%2A%282%2F3%29%2A%28n%2F24%29\" = 13.\r\n" );
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document.write( "Simplify and find n\r\n" );
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document.write( "      \"%282%2F3%29%2A%28n%2F24%29\" = 13*2 = 26;\r\n" );
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document.write( "         n    = \"%2826%2A24%2A3%29%2F2\" = 936.\r\n" );
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document.write( "ANSWER.  The total sweets was 936.\r\n" );
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document.write( "The number of giving away children is 8;\r\n" );
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document.write( "the number of receiving is 16, two times as 8.\r\n" );
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document.write( "Each of 8 children gives away  2/3  of sweets.\r\n" );
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document.write( "Actually, every of 8 children gives (1/3) of what he (or she) has to two of 16 children.\r\n" );
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document.write( "Thus the increment for each of 16 is  \"1%2F3\"  of what everybody has at the beginning.\r\n" );
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document.write( "This one third is 13, according to the problem.\r\n" );
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document.write( "Hence, every child had 3*13 = 39 sweets at the beginning.\r\n" );
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document.write( "So the total sweets is  39*24 = 936.    ! The same answer !\r\n" );
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