Final answer:
The father's present age is 98 years and the son's present age is 35 years.
Step-by-step explanation:
To find their present ages, let's start by assigning variables. Let the father's present age be represented by 'F' and the son's present age be represented by 'S'.
We're given that 14 years ago, the father was four times as old as his son. This can be written as the equation: F - 14 = 4(S - 14).
We're also given that the father's present age is two times the age of his son will be in the future. This can be written as the equation: F = 2(S + 14).
To solve these equations, we can use substitution. First, solve the second equation for F in terms of S: F = 2S + 28.
Now substitute this expression for F in the first equation: 2S + 28 - 14 = 4(S - 14).
Simplify and solve for S: 2S + 14 = 4S - 56. Rearrange this equation to: 2S - 4S = -56 - 14. Simplify further: -2S = -70. Divide both sides by -2 to solve for S: S = 35.
Now substitute this value for S back into the second equation to find F: F = 2(35 + 14) = 2 * 49 = 98.
Therefore, the father's present age is 98 years and the son's present age is 35 years.