Answer:
the numbers are 3, 5, 4
Explanation:
The given relations can be written as a system of equations. These are conveniently solved using elimination.
Setup
Let the three numbers be represented by x, y, z. The given relations are ...
x +y +z = 12
x -y +z = 2
x +y -z = 4
Solution
Subtracting the second equation from the first gives ...
(x +y +z) -(x -y +z) = (12) -(2)
2y = 10 . . . . . . . . . simplify
y = 5 . . . . . . . . divide by 2
Subtracting the third equation from the first gives ...
(x +y +z) -(x +y -z) = (12) -(4)
2z = 8 . . . . . . . . . simplify
z = 4 . . . . . . . . divide by 2
Using these values of y and z in the first equation lets us find x:
x +5 +4 = 12
x = 3 . . . . . . . . . subtract 9
The numbers, in order, are (3, 5, 4).