From the condition, you have B = S + 3, 3B = M, F = M + 4, 4S = F. Then moving from the bottom to the top and making substitutions, you get this chain of equalities 4S = F = M + 4 = 3B + 4 = 3*(S+3) + 4. which gives you 4S = 3*(S+3) + 4 ====> 4S = 3S + 13 ====> S= 13. The sister is 13 years old. Ben is 13 + 3 = 16 years old. The mother is 3*16 = 48 years old and the father is 52 years old.