The brother is elder to his sister by 6 years. Seven years ago the product of their age was 72.what is the age of brother.
(b-7)(s-7) = 72
b = s+6
so
(s+6-7)(s-7) = 72
(s-1)(s-7) = 72
s^2 - 8 s + 7 = 72
s^2 - 8 s - 65 = 0
(s-13)(s+5) = 0
s = 13
then b = 19
To find the age of the brother, we can solve the problem step by step.
Let's say the brother's age is B and the sister's age is S.
According to the problem, the brother is elder to his sister by 6 years. Therefore, we can write the equation:
B = S + 6 ----- (Equation 1)
Seven years ago, the product of their ages was 72. So, we need to subtract 7 from both the brother's and sister's ages and multiply them together:
(B - 7)(S - 7) = 72 ----- (Equation 2)
We can use Equation 1 to substitute the value of B in Equation 2:
(S + 6 - 7)(S - 7) = 72
(S - 1)(S - 7) = 72
Expanding the equation:
S^2 - 7S - S + 7 = 72
S^2 - 8S + 7 - 72 = 0
S^2 - 8S - 65 = 0
Now, we can solve this quadratic equation to find the value of S (the sister's age).
Using factorization or the quadratic formula, we can find that the two values of S are S = -5 and S = 13.
Since age cannot be negative, we discard S = -5.
Therefore, the sister's age, S = 13.
Now, substituting the value of S in Equation 1, we can find the brother's age, B:
B = S + 6
B = 13 + 6
B = 19
So, the age of the brother is 19.