casey is six time as old as Ralph, In two years, she will be four time as old as Ralph. How old is each of them now?

Statement 1: Casey is 6 times as old as Ralph gives

C = 6R

where C and R represent Casey and Ralph's current ages respectively.

Statement 2: In 2 years, Casey will be four times as old as Ralph gives

C + 2 = 4 (R + 2)

Expanding the brackets gives

C + 2 = 4R + 8

Substituting in C from the first equation gives

6R + 2 = 4R + 8

Which can be rearranged as

2R = 6

Implying R = 3 and C = 6R = 18

Therefore, Ralph is 3; Casey is 18