three years ago, a father was three times as old as his son. In three years time the sum of their aged will be 76 years. Determine their present ages

Answer 1

Let's assign variables to the present ages of the father and son. Let f be the father's age and s be the son's age.

According to the problem, three years ago, the father was three times as old as his son:

f - 3 = 3(s - 3) [Equation 1]

In three years time, the sum of their ages will be 76 years:

(f + 3) + (s + 3) = 76 [Equation 2]

Now, let's solve the system of equations:

Expanding equation 1, we get:

f - 3 = 3s - 9
f - 3s = -6 [Equation 3]

Rearranging equation 2, we get:

f + s = 76 - 6
f + s = 70 [Equation 4]

Using equations 3 and 4, we can solve for f and s.

Multiply equation 3 by -1:

-f + 3s = 6 [Equation 5]

Add equations 4 and 5:

f + s + (-f + 3s) = 70 + 6
4s = 76
s = 19

Substituting the value of s into equation 4:

f + 19 = 70
f = 70 - 19
f = 51

Therefore, the father is currently 51 years old and the son is currently 19 years old.