If M is Melissa's age now then Jennifer's age is M-7.
In 4 years' time their ages will be respectively M+4 and M-7+4=M-3.
Half of Melissa's age 4 years hence=(M+4)/2. One year older than this is (M+4)/2+1=(M+6)/2.
So M-3 (Jessica's age in 4 years)=(M+6)/2,
2(M-3)=M+6,
2M-6=M+6, 2M-M=6+6,
M=12 (Melissa is 12 years old now) and Jennifer is 7 years younger=12-7=5 years old.
CHECK
4 years from now Melissa will be 16 and Jennifer will be 9.
Half of Melissa's age will be 8 and 1 more than this makes 9, which will be Jennifer's age.