The mother's age is 8 times her son's age. After 6 years, the age of the mother will be 9/2 times her son's age. The present ages of the son and the mother are, respectively

Son's present age is 6.

Mother's present age is 48.

Step-by-step explanation:

Let the mother age be x.

Let the son's age be y.

x = 8y

x + 6 = 9/2 * (y + 6)

Put x as 8y in the second equation and solve for y.

8y + 6 = 9/2 (y + 6)

8y + 6 = 9/2y + 27

8y - 9/2y = 27 - 6

7/2y = 21

y = 21 * 2/7

y = 42/7

y = 6

Put y as 6 in the first equation and solve for x.

x = 8 (6)

x = 48

son = 6 mother = 48

Step-by-step explanation:

Mother = m

son = s

m = 8s

m+6 = 9/2 * (s+6)

so

2 (8s + 6) = 9 (s + 6)

16s + 12 = 9s + 54

16s - 9s = 54 - 12

7s = 42

s = 42/7 = 6 years old

so the mother is 8s = 8*6 = 48 years old