SOLUTION: The sum of three numbers is 32 the difference between the largest and the smallest number is 17. The sum of the two smaller numbers is 13 find the numbers

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Question 420001: The sum of three numbers is 32 the difference between the largest and the smallest number is 17. The sum of the two smaller numbers is 13 find the numbers
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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Three numbers, x, y, z (x is the smallest)
:
The sum of three numbers is 32
x + y + z = 32
:
the difference between the largest and the smallest number is 17.
z - x = 17
z = (x+17)
:
The sum of the two smaller numbers is 13
x + y = 13
y = (-x+13)
:
find the numbers
Replace z and y in the 1st equation
x + (-x+13) + (x+17) = 32
Combine like terms
x - x + x + 13 + 17 = 32
x + 30 = 32
x = 32 - 30
x = 2 is the smallest number
then
y = -2 + 13
y = 11
and
z = 2 + 17
z = 19 is the largest number
:
:
Check solutions
2 + 11 + 19 = 32