Question

A mother has 7 children. The mean age of the children is 13 years 2 months. If the mother's age is included, the mean age rises to 17 years 7 months.calculate the age of the mother

Answer 1

Mean age of 7 children=sum of ages of 7 children/7
13 years 2 months=sum of 7 children/7
Sum of ages of 7 children=7×13 years 2 months
=91 years 14 months
=91 years+1 year 2 months
=92 years 2 months

Mean age of 7 children +1mother= sum of ages of 7 children+1 mother/8

17 years 7 months= sum of ages of 8 children/8
Sum of ages of 8 children=8×17 years 7 months
=136 years 56 months
=136 years+ 4 years 8 months
= 140 years 8 months
Therefore: age of mother= 140 years 8 months -92 years 2 months
= 48 years 6 months

Answer 2

Let M be the age of the mother.

The total age of the 7 children is 7 * 13 years 2 months = 91 years 14 months.

The total age of the mother and the 7 children is M + 91 years 14 months.

According to the second scenario, the total age of the mother and the 7 children is 8 * 17 years 7 months = 139 years 4 months.

Therefore, we can set up the equation:

M + 91 years 14 months = 139 years 4 months
M + 91 years + 14 months = 139 years + 4 months
M + 91 years = 139 years - 14 months
M = 48 years - 14 months
M = 47 years 10 months

Therefore, the age of the mother is 47 years 10 months.

Answer 3

Apologies for my error in the calculation earlier. Your correction is correct. The age of the mother should indeed be 48 years 6 months. Thank you for pointing that out.