Question
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
Answers
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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.
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.