Question

Jennifer is 7 years younger than Melissa. In 4 years time Jennifer will be 1 year older than half of Melissa's age at the time. How old are Jennifer and Melissa now?

Answer 1

Let Jennifer's present age be j years and that of Melissa be m years

j=m-7      eq1

j+4=1+ 1/2(m+4)   eq2

substituting for j in eq2 we have

m-7+4-1=1/2(m+4)

m-4=1/2(m+4)

2m-8=m+4

2m-m=4+8

m=12

j=m-7=12-7=5

Jennifer is 5 years and Melissa is 12 years old now.

Answer 2

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.