<PRE><B>Question 420001</B>
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</PRE>