Let the mother's age be x

Let the daughter's age be y

x+y=32

y=32-x (subsitution)

Maxmium value = 32:

In four years their ages:

y+4 and x+4

Formal equation:

(x+4)-(y+4)=24

x-y=24

Apply subsitution:

x-(32-x)=24

2x-32=24

2x=56

x=28

y=32-28

y=4

Hence, the mother's age is 28 and the daugther's age is 4.

Paul. 

RELATED QUESTIONS

A mother is 28 years older than her daughter. In 5 years the sum of their ages will be... (answered by Alan3354,josgarithmetic)

1) A father is five times as old as his son. If the difference in their ages is 32 years,  (answered by ikleyn)

five years from now, the sum of the ages of a woman and her daughter will be 40 years.... (answered by stanbon)

the sum of the ages of a mother and daughter is 75 and the difference in their ages is 29  (answered by ikleyn)

rose is thrice as old as her daughter .In 5 years to come the sum of their ages will be... (answered by ewatrrr)

1) A mother is five times as old as her daughter. If the sum of their ages 6 years ago... (answered by addingup)

Ten years ago, the sum of the ages of a mother and her daughter was seventy years. This... (answered by josgarithmetic,MathTherapy)

The sum of the ages of Mrs Bai and her daughter Jenni is 70. The difference between their  (answered by chitra)

a mother and daughter decided to add their ages together. the sum of their ages is 76.... (answered by josgarithmetic)