Average weight of children and mother: $\frac{C_1 + C_2 + M}{3} = 50$ Multiply by 3: $C_1 + C_2 + M = 150$ (Equation 1)

Average weight of children and father: $\frac{C_1 + C_2 + F}{3} = 52$

Multiply by 3: $C_1 + C_2 + 60 = 156$ (Equation 2)

From Equation 2, $C_1 + C_2 = 96$

Substitute $C_1 + C_2 = 96$ into Equation 1: $96 + M = 150$

Solving for M: $M = 150 - 96 = 54$