document.write( "Question 1179051: The sum of three distinct whole numbers is 100. Each of the three numbers contains at least one digit 6. What is the greatest of the three numbers? \n" ); document.write( "

Algebra.Com's Answer #808544 by ikleyn(52835) $\"\"$ $\"About$

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\n" ); document.write( "The sum of three distinct whole numbers is 100.
\n" ); document.write( "Each of the three numbers contains at least one digit 6.
\n" ); document.write( "What is the greatest of the three numbers?
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document.write( "The greatest number is 68.      ANSWER\r\n" );
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document.write( "Two other numbers are 16 and 16.\r\n" );
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document.write( "CHECK.  68 + 16 + 16 = 100.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved. Easy mental exercise.\r
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\n" ); document.write( "\n" ); document.write( " Explanation\r
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document.write( "In order for the greater number would be greatest possible, two other numbers should be smallest possible.\r\n" );
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document.write( "So, we consider several smaller number pairs  (6,6),  (6,16),  (16,6)  and (16,16).\r\n" );
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document.write( "The pair  (6,6)  has the sum 12, leaving  100-12 = 88 for the greater number, which does not work.\r\n" );
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document.write( "The pair  (6,16)  has the sum 22, leaving  100-22 = 78 for the greater number, which does not work.\r\n" );
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document.write( "The pair  (16,6) is the same as (6,16), i.e. does not work.\r\n" );
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document.write( "Finally, the pair (16,16) has the sum 32, leaving  100-32 = 68 for the greater number,  which  DOES WORK,  fortunately.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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\n" ); document.write( "\n" ); document.write( "Easy mental exercise.\r
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