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
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.
Let's assume the current age of the son is represented as "x" and the current age of the father is represented as "y".
According to the given information,
"Three years ago, a father was three times as old as his son" can be written as:
y - 3 = 3(x - 3)
"In three years time, the sum of their ages will be 76 years" can be written as:
(x + 3) + (y + 3) = 76
We can now solve the system of equations:
1. y - 3 = 3x - 9 (Equation 1)
2. x + 3 + y + 3 = 76 (Equation 2)
From Equation 1, we can rewrite it as:
y = 3x - 6
Substituting this value of y in Equation 2, we get:
x + 3 + (3x - 6) + 3 = 76
4x = 76 - 9 + 6 - 3
4x = 70
x = 70 / 4
x = 17.5
Since the ages must be whole numbers, we can conclude that the given information may have some error or missing values. Please double-check the problem statement and provide the correct information.