If  P  is the value of the principal amount (which is the same in both certificates),

then from the condition you have these two equations


    350 = P*r           (1)


    550 = P*(r+0.04)    (2)


where "r" is the unknown smaller rate.


Subtract equation (1) from equation (2).  You will get


    200 = P*0.04.


Hence, the principal is  P =  = 5000 dollar.


Now from equation (1) you can find the smaller rate


    350 = 5000*r,

    r =  = 0.07.


ANSWER.  The lower rate is 7%.  The higher rate is 11%.