cool problem
x and y are the digits
x+y=11
yx=2(xy)+34
I'm not sure how to solve this using legit math so use trial and error
the 1 digit numbers that could be possible are
9,2
8,3
7,4
6,5
5,6
4,7
3,8
2,9
all of them add up to 11
the pairs obtained by swiching the number are
92 and 29
83 and 38
74 and 47
65 and 56
we find which ones are equal when we subtract 34 from the larger number and divide by 2
92-34=58
58/2=29
92 and 29 work
83-34=49
49/2=24.5 not equal to 38 not work
74-34=40
40/2=20 47 not equal to 20 so doesn't work
65-34=31
31/2=15.5 not equal to 56 so doesn't work
the origonal number is 29