document.write( "Question 1154011: The sum of three numbers is 17. Two times the smallest is 4 less than the largest, while the sum of the largest and smallest is 10. Use a linear system in three variables to find the three numbers. \n" ); document.write( "

Algebra.Com's Answer #776368 by ramkikk66(644) $\"\"$ $\"About$

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Let the smallest number be x and largest be y\r
\n" ); document.write( "\n" ); document.write( "Given that
\n" ); document.write( "Two times the smallest is 4 less than the largest,
\n" ); document.write( " $\"2x+=+y+-+4\"$ --- (1)
\n" ); document.write( "sum of the largest and smallest is 10
\n" ); document.write( " $\"x+%2B+y+=+10\"$ ---- (2)\r
\n" ); document.write( "\n" ); document.write( "Let us solve the 2 simultaneous equations above.\r
\n" ); document.write( "\n" ); document.write( "(1) can be rewritten as
\n" ); document.write( " $\"2x+-+y+=+-4\"$ --- (3)\r
\n" ); document.write( "\n" ); document.write( "We have a +y in (2) and a (-y) in (3) so we can eliminate y by adding the 2 equations.\r
\n" ); document.write( "\n" ); document.write( "Adding (2) and (3) gives
\n" ); document.write( " $\"x+%2B+y+%2B+2x+-+y+=+10+-+4\"$
\n" ); document.write( " $\"3x+=+6\"$ or $\"x+=+2\"$ \r
\n" ); document.write( "\n" ); document.write( "Since $\"x+%2B+y+=+10\"$ , $\"y+=+8\"$
\n" ); document.write( "So the smallest number is 2, largest is 8\r
\n" ); document.write( "\n" ); document.write( "Also given that sum of 3 numbers is 17. Let the middle number be m.
\n" ); document.write( " $\"2+%2B+m+%2B+8+=+17\"$ gives $\"m+=+7\"$ \r
\n" ); document.write( "\n" ); document.write( "So the 3 numbers are $\"2\"$ $\"7\"$ and $\"8\"$ \r
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