A - M = 5,                 (1)
(A+6) + (M+6) = 35.        (2)

--->

A - M =  5,                (3)
A + M = 23.                (4)

Add the two equations (3) and (4) (both sides) and see what will happen.

Let Ann's age be A

Then Melissa's is: A - 5

We then get the following SUM-OF-AGES equation: A + 6 + A - 5 + 6 = 35

2A + 7 = 35

2A = 28

A, or Ann is: 

Melissa is:  

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