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Here is your solution:
y must be one because y is the carry from the addition of the digits at tens position. That means z = 2.
Now the result of the addition is 122.
We get this equation:
2 * (10x+1) = 122; [xy means 10*x+1]
=> x = 3
So x+y+z = 3+1+2 = 6
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