document.write( "Question 1096018: There is a report in the meeting room. If 4 people sit per bench 1 extra bench is needed. If 6 people sit per bench 4 benches are left vacant. How many people are attending the report. \r
\n" ); document.write( "\n" ); document.write( "I believe it’s 12 but need help putting in an equation. \n" ); document.write( "

Algebra.Com's Answer #710488 by ikleyn(52780) $\"\"$ $\"About$

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document.write( "Let n be the number of people and \"b\" be the number of benches.\r\n" );
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document.write( "Then the condition gives you these two equations:\r\n" );
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document.write( " = b + 1,    (1)\r\n" );
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document.write( " = b - 4.    (2)\r\n" );
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document.write( "It is literal translation of the condition to equations.\r\n" );
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document.write( "You can rewrite eqs (1) and (2) in the form\r\n" );
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document.write( "n = 4b +  4,         (1')\r\n" );
document.write( "n = 6b - 24.         (2')\r\n" );
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document.write( "It implies 4b + 4 = 6b - 24  ====>  24 + 4 = 6b - 2b   ====>  2b = 28  ====>  b= 14.\r\n" );
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document.write( "Then n = 4b + 4 = 4*14 + 4 = 60.\r\n" );
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document.write( "Answer.  60 people and 14 benches.\r\n" );
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document.write( "Check.   60/4 = 15 = 14+1  <====>  1 extra bench.\r\n" );
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document.write( "         60/6 = 10  <====>  4 benches are vacant.     ! Correct !\r\n" );
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