document.write( "Question 1121978: there were 48 entries from Grade 1 and Grade 2 in a storytelling competition. The rest were from Grade 3. If 30 entries were not from Grade 1 and 28 entries were not from Grade 2, how many entries were there altogether? \n" ); document.write( "

Algebra.Com's Answer #738022 by ikleyn(52786) $\"\"$ $\"About$

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document.write( "x = from Grade 1\r\n" );
document.write( "y - from Grade 2\r\n" );
document.write( "z = from Grade 3\r\n" );
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document.write( "x+y = 48    (1)     (\"there were 48 entries from Grade 1 and Grade 2\")\r\n" );
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document.write( "y+z = 30,   (2)     {\"30 entries were not from Grade 1\")\r\n" );
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document.write( "x+z = 28.   (3)     (\"28 entries were not from Grade 2\")\r\n" );
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document.write( "Add equations (1) and (2). You will get\r\n" );
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document.write( "x + 2y + z = 48 + 30 = 78.    (4)\r\n" );
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document.write( "In equation (4), replace (x+z) by 28, based on eq(3). You will get\r\n" );
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document.write( "28 + 2y = 78  ====>  2y = 78-28 = 50  ====>  y = 50/2 = 25.\r\n" );
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document.write( "Now from equation (1),  x = 48-25 = 23.\r\n" );
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document.write( "    From equation (2),  z = 30-25 =  5.\r\n" );
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document.write( "Answer.  x= 23;  y= 25;  z= 5.  x + y + z = 23 + 25 + 5 = 53.\r\n" );
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document.write( "         53 entries altogether.\r\n" );
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