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Answer:
middle brother = x
older brother = x+1
younger brother = x-1
x-1+x+x+1=129
3x+0=129
3x=129
x = 43(middle brother)
43-1 = 42(younger brother)
43+1 = 44(elder brother)
Check:
43-1+43+43+1=129
42+43+44=129
129=129