document.write( "Question 1167409: A survey carried out recently to find the number of applicants that applied for jobs into 3 newspaper establishment, revealed that 70 applied to daily times, 65 applied to Daily graphics and 85 applied to daily punch. 40 applied to daily times only, 20 applied to daily graphics only while 45 applied to daily punch only. If 15 applied to all three newspaper establishment, find:The number that applied to both daily times and daily graphics \n" ); document.write( "

Algebra.Com's Answer #792055 by ikleyn(52781) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( "This problem came to the forum several years ago, and I solved it at that time, see the link\r
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\n" ); document.write( "\n" ); document.write( "https://www.algebra.com/algebra/homework/sets-and-operations/sets-and-operations.faq.question.1101879.html \r
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document.write( "Given:  DT (marked \"T\"),  70 & 40 (red circle).\r\n" );
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document.write( "        DG (marked \"G\"),  65 & 20 (green circle).\r\n" );
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document.write( "        P,                85 & 45 (blue circle).\r\n" );
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document.write( "                 Venn diagram \r\n" );
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document.write( "Given:     T (70 & 40),  G (65 & 20)  and  P (85 & 45).\r\n" );
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document.write( "Unknowns:  x,  y,  and  z.\r\n" );
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document.write( "Solution\r\n" );
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document.write( "x + y + 15 + 40 = 70\r\n" );
document.write( "y + z + 15 + 45 = 85\r\n" );
document.write( "x + z + 15 + 20 = 65\r\n" );
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document.write( "x + y = 15,       (1)\r\n" );
document.write( "y + z = 25,       (2)\r\n" );
document.write( "x + z = 30.       (3)\r\n" );
document.write( "------------------------Add 3 equations  ====>\r\n" );
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document.write( "2x + 2y + 2z = 15 + 25 + 30 = 70  ====>\r\n" );
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document.write( "x + y + z = 35.   (4)\r\n" );
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document.write( "Subtract  (1)  from (4):  z= 20;\r\n" );
document.write( "Subtract  (2)  from (4):  x= 10;\r\n" );
document.write( "Subtract  (3)  from (4):  y=  5.\r\n" );
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document.write( "INTERMADIATE ANSWER:  x= 10;  y= 5;  z= 20.\r\n" );
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document.write( "FINAL ANSWER:         x + 15 = 10 + 15 = 25.\r\n" );
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document.write( "      25 applicants applied to BOTH  Daily times and Daily graphics.\r\n" );
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