document.write( "Question 1061323: The average of 5 distinct whole numbers is 8. When the least number is replaced by a second copy of the largest number, the average is increased to 9.2. What is the largest possible number? \n" ); document.write( "

Algebra.Com's Answer #676107 by KMST(5328) $\"\"$ $\"About$

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For the 5 original conservative integers,
\n" ); document.write( " $\"sum=5%2A8=40\"$
\n" ); document.write( "Replacing the least number, $\"x\"$ , with the largest one, $\"y\"$ ,
\n" ); document.write( "the new sum is $\"40-x%2By=5%2A9.2\"$ --> $\"40-x%2By=46\"$ --> $\"y=x%2B6\"$
\n" ); document.write( "The other 3 numbers, $\"x%2Ba\"$ , $\"x%2Bb\"$ , and $\"x%2Bc\"$ are in between.
\n" ); document.write( "The sum of all 5 numbers is
\n" ); document.write( " $\"x%2B%28x%2B6%29%2B%28x%2Ba%29%2B%28x%2Bb%29%2B%28x%2Bc%29=40\"$
\n" ); document.write( " $\"5x%2B%286%2Ba%2Bb%2Bc%29=40\"$ ,
\n" ); document.write( "Since $\"5x\"$ and $\"40\"$ are both multiples of $\"5\"$ ,
\n" ); document.write( " $\"6%2Ba%2Bb%2Bc\"$ must also be a multiple of $\"5\"$ .
\n" ); document.write( "Since all the numbers are different,
\n" ); document.write( " $\"1%2B2%2B3%3C=a%2Bb%2Bc%3C=3%2B4%2B5\"$ <---> $\"6%3C=a%2Bb%2Bc%3C=12\"$ ,
\n" ); document.write( "so $\"12%3C=6%2Ba%2Bb%2Bc%3C=18\"$ .
\n" ); document.write( "The only multiple of $\"5\"$ between $\"12\"$ and $\"18\"$
\n" ); document.write( "is $\"15\"$ , so $\"6%2Ba%2Bb%2Bc=15\"$ ,
\n" ); document.write( " $\"5x%2B15=40\"$ --> $\"5x=40-15=25\"$ --> $\"x=25%2F5=5\"$ , and
\n" ); document.write( " $\"y=5%2B6=highlight%2811%29\"$ . \n" ); document.write( "

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