Five years ago, a father was 3 times as old as his son. Now, their combined ages amount to 110 years. Thus, the present age of the father is?
5 years ago:
son's age --- x
father's age -- 3x
now:
son's age = x+5
fathers's = 3x+5
x+5 + 3x+5 = 110
solve for x, then sub into 3x+5
To solve this problem, we can use algebraic equations to represent the information given in the question.
Let's assume that the current age of the son is S years, and the current age of the father is F years.
According to the information given, five years ago, the father was 3 times as old as his son. This can be represented as:
F - 5 = 3(S - 5) (equation 1)
Now, the combined ages of the father and son amount to 110 years. This can be represented by:
F + S = 110 (equation 2)
To solve these two equations simultaneously, we can start by rearranging equation 1 to solve for F:
F - 5 = 3S - 15
F = 3S - 10
Next, substitute this expression for F in equation 2:
3S - 10 + S = 110
Combine like terms:
4S - 10 = 110
Add 10 to both sides:
4S = 120
Divide both sides by 4:
S = 30
Now, we can substitute the value of S back into equation 2 to find the age of the father, F:
F + 30 = 110
Subtract 30 from both sides:
F = 80
Therefore, the present age of the father is 80 years.