SOLUTION: 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 t

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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.
Answer by ramkikk66(644) About Me  (Show Source):
You can put this solution on YOUR website!
Let the smallest number be x and largest be y
Given that
Two times the smallest is 4 less than the largest,
2x+=+y+-+4 --- (1)
sum of the largest and smallest is 10
x+%2B+y+=+10 ---- (2)
Let us solve the 2 simultaneous equations above.
(1) can be rewritten as
2x+-+y+=+-4 --- (3)
We have a +y in (2) and a (-y) in (3) so we can eliminate y by adding the 2 equations.
Adding (2) and (3) gives
x+%2B+y+%2B+2x+-+y+=+10+-+4
3x+=+6 or x+=+2
Since x+%2B+y+=+10, y+=+8
So the smallest number is 2, largest is 8
Also given that sum of 3 numbers is 17. Let the middle number be m.
2+%2B+m+%2B+8+=+17 gives m+=+7
So the 3 numbers are 2 7 and 8