Question

In fourteen years time,a mother will be twice as old as her son. four years ago the sum of their ages was 30years, find how old the mother was when the son was born​?

Answer 1

By setting up equations to represent the given statements and solving them, we find that the son is currently 8 years old and the mother is 30 years old. Therefore, the mother was 22 years old when her son was born.

Step-by-step explanation:

To solve this problem, we need to set up equations based on the information given:

1. In fourteen years, the mother will be twice as old as her son.
2. Four years ago, the sum of their ages was 30 years.

Let's define M as the mother's current age and S as the son's current age.

Based on the first piece of information, we can write the equation: M + 14 = 2(S + 14).

From the second piece of information, we get the equation: (M - 4) + (S - 4) = 30.

Now, we solve the system of equations. First, we simplify the second equation:

M - 4 + S - 4 = 30

M + S - 8 = 30

M + S = 38

Next, we solve the first equation for M:

M + 14 = 2S + 28

M = 2S + 14

Now, substitute M in the second equation:

(2S + 14) + S = 38

3S + 14 = 38

3S = 24

S = 8

Now find M:

M = 2S + 14

M = 2(8) + 14

M = 30

The mother's age when the son was born is the current age of the mother minus the current age of the son:

30 (Mother's current age) - 8 (Son's current age) = 22 years.

Therefore, the mother was 22 years old when her son was born.