Bob has $X$ dollars now. If Pat gives Bob a dollar, Bob will have twice as many dollars as Pat. If Bob gave Pat a dollar instead, they both

Let p = amount of money that Pat has.

Let b = amount of money that Bob has.

If Pat gives Bob a dollar, then Pat will have p - 1 dollars and Bob will have b + 1 dollars.

Since Bob will have twice as much money as Pat has:  b + 1  =  2(p - 1).

If Bob gives Pat a dollar, then Pat will have p + 1 dollars and Bob will have b - 1 dollars.

Since they will then have the same amount of money:  p + 1  =  b - 1.

Putting these two equations together:

b + 1  =  2(p - 1)   --->   b + 1  =  2p - 2   --->   3  =  2p - b

b - 1  -  p + 1         --->                                       -2  =    p - b

2p - b  =  3    --->                     2p  - b  =  3

  p - b  =  -2   --->   x -1   --->   -p + b  =  2

Adding down the columns:                  p  = 5

Substituting back into an equation:     b  =  7