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 #808558 by greenestamps(13203) $\"\"$ $\"About$

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\n" ); document.write( "The three numbers are either 1- or 2-digit numbers, because their sum is 100.

\n" ); document.write( "There can't be two numbers in the 60s, because the sum would be more than 100.

\n" ); document.write( "Since each number must have at least one 6, there is one number in the 60s.

\n" ); document.write( "The other two numbers have to have units digit 6, because their tens digits are not 6.

\n" ); document.write( "To make a sum of 100, the units digit of the number in the 60s must be 8.

\n" ); document.write( "So one of the numbers is 68. Then the other two have a sum of 100-68=32; they both have units digit 6, and they are different numbers. There is only one possibility -- the other two numbers are 6 and 26.

\n" ); document.write( "ANSWER: The largest number is 68.

\n" ); document.write( "Note since the problem asked only for the largest of the three numbers, we did not need to find the two smaller numbers. But doing so makes the problem a bit more interesting.

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