Five years ago mother's age was square of her son. 10 years hence her age will be twice of her son's age.
Find mother's age.
(m-5) = (s-5)^2
m+10 = 2(s+10)
Now you can find m and s. You will get two answers, but only one is possible, given the conditions above.
To find the mother's age, we need to solve the problem using algebraic equations. Let's denote the current age of the mother as M and the current age of her son as S.
According to the problem, five years ago the mother's age was the square of her son's age. So, we can write the first equation as:
M - 5 = (S - 5)^2
Also, it is given that 10 years hence, the mother's age will be twice her son's age. We can write the second equation as:
M + 10 = 2(S + 10)
Now, we have a system of two equations with two variables. Let's solve them to find the values of M and S.
First, let's expand the equation M - 5 = (S - 5)^2:
M - 5 = S^2 - 10S + 25
M = S^2 - 10S + 30 ---- Equation 1
Next, let's solve the equation M + 10 = 2(S + 10):
M + 10 = 2S + 20
M = 2S + 10 ---- Equation 2
Now, substitute the value of M from Equation 2 into Equation 1:
2S + 10 = S^2 - 10S + 30
Rearrange the equation to bring all terms to one side:
S^2 - 12S + 20 = 0
We have a quadratic equation. Now, we can solve this equation using factoring, completing the square, or the quadratic formula. In this case, we can factor the equation as:
(S - 2)(S - 10) = 0
This gives us two possible solutions for S:
S = 2 or S = 10
However, since the problem is asking for the mother's age, we need to evaluate M using Equation 2:
If S = 2, then M = 2(2) + 10 = 14.
If S = 10, then M = 2(10) + 10 = 30.
Therefore, the mother's age can be either 14 or 30.