Me ! two lifeguards pull on ropes attached to a
raft. if they pull in the same direction, the raft
experiences a net external force of 352 n to
the right. if they pull in opposite directions,
the raft experiences a net external force of
157 n to the left.
answer in units of n.
what is the magnitude of the smaller of the
individual forces?
answer in units of n.

When both pull in the same direction, their net is 352.
When they pull in opposite directions, the net in one direction is 157.

If you want to set up the system of equations,
you should start with

                                   A + B  =  352
                                   A  - B  =  157 .

then add them, etc.

You'll find that

-- Guy-A is the stronger one. 
   He's the one who moves to the other side,
   and he pulls with  254.5 newtons both times.

-- Guy-B is the less strong one.
   He stays put, and pulls with 97.5 newtons.
 

The answer is frictional force