in fourteen years time a mother will be twice as old as her son .four years ago th sum of tier was 30 years.find how old was the mother when the son was born
m+14 = 2 (s+14)
m -4 + s-4 = 30
m + 14 = 2s + 28
m + s = 38
-----------------------------subtract
0 +14 - s = 2 s - 10
24 = 3 s
s = 8
so m = 30
so m is 22 years older than s
Please can you explain how to do the sum
thanks allot
To solve this problem, let's assign variables to the ages of the mother and the son.
Let's assume the current age of the son is S years, and the current age of the mother is M years.
According to the problem, in fourteen years, the mother will be twice as old as her son. So we can write the equation:
M + 14 = 2(S + 14)
Now let's consider the second statement. Four years ago, the sum of their ages was 30 years. So we can write another equation:
(M - 4) + (S - 4) = 30
Now we have a system of two equations. We can solve it to find the ages of the mother and son.
Let's start by solving the second equation for one of the variables. We'll solve for M:
M - 4 = 30 - (S - 4)
M - 4 = 34 - S + 4
M = 38 - S
Now substitute this expression for M into the first equation:
38 - S + 14 = 2(S + 14)
Simplify:
52 - S = 2S + 28
Add S to both sides:
52 = 3S + 28
Subtract 28 from both sides:
24 = 3S
Divide both sides by 3:
S = 8
Now that we know the current age of the son is 8, we can find the current age of the mother:
M = 38 - S
M = 38 - 8
M = 30
Therefore, the current age of the mother is 30 and the son is 8.
To find out how old the mother was when the son was born, we need to subtract 8 years from her current age:
30 - 8 = 22
So, the mother was 22 years old when the son was born.