document.write( "Question 1189249: A factory sorts pencils into bags such that 19 large bags plus 3 small bags contain a total of 224 pencils. The sum of the number of pencils in a large bag plus the number in a small bag is:
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Algebra.Com's Answer #820576 by ikleyn(52790) $\"\"$ $\"About$

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\n" ); document.write( "A factory sorts pencils into bags such that 19 large bags plus 3 small bags contain a total of 224 pencils.
\n" ); document.write( "The sum of the number of pencils in a large bag plus the number in a small bag is:
\n" ); document.write( "A)16 B)36 c)42 D)19 E)18
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\n" ); document.write( "\n" ); document.write( "            Now, when you have so many solutions from different tutors, it should be clear \r
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\n" ); document.write( "\n" ); document.write( "            Consider this one below.\r
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document.write( "Let x be the number of pencils in a large bag and y be the number of pencils in a small bag.\r\n" );
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document.write( "Then you have this equation\r\n" );
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document.write( "    19x + 3y = 224      (1)\r\n" );
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document.write( "and this inequality\r\n" );
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document.write( "    x > y               (2)\r\n" );
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document.write( "Equation (1) should be solved in whole numbers.\r\n" );
document.write( "Inequality (2) is the math translation of the terms \"large bag\" and \"small bag\".\r\n" );
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document.write( "Using inequality (2), we get the following inequality from equation (1)\r\n" );
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document.write( "    19x + 3x > 224,    or    22x > 224,  \r\n" );
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document.write( "It gives  x >  = 10.1818...,  and since x should be whole number, it implies  x >= 11.\r\n" );
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document.write( "So, we need find the solution to equation (1) in whole numbers x, y with  x >= 11.\r\n" );
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document.write( "There are not so many such possibilities:  19*11 = 209  and  19*12 = 228,\r\n" );
document.write( "so the only real candidate is  x = 11.\r\n" );
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document.write( "It gives  y =  =  =  = 5,  which is a whole number.\r\n" );
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document.write( "So, the problem has a UNIQUE solution  x= 11,  y= 5,  which gives the sum  x + y = 11 + 5 = 16.\r\n" );
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document.write( "ANSWER.  The number of pencils in a large bag plus the number in a small bag is 16  (option (A) ).\r\n" );
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