Three years ago, a father was three times as old as his son. In five years time, the father will be twice as old as his son. What is the sum of their ages in four years time?
Let's denote the present age of the father as F and the present age of the son as S.
According to the first statement, three years ago, the father was three times as old as his son:
F - 3 = 3(S - 3)
F - 3 = 3S - 9
F = 3S - 6
According to the second statement, in five years time, the father will be twice as old as his son:
F + 5 = 2(S + 5)
F + 5 = 2S + 10
F = 2S + 5
Now, we can equate both equations to find the ages of the father and son. So:
3S - 6 = 2S + 5
3S - 2S = 5 + 6
S = 11
Substituting the value of S back into the second equation:
F = 2(11) + 5
F = 22 + 5
F = 27
In four years time, the son will be 11 + 4 = 15 years old, and the father will be 27 + 4 = 31 years old. The sum of their ages in four years time will be 15 + 31 = 46.
Therefore, the sum of their ages in four years time is 46.
Let's represent the current age of the son as "s" and the current age of the father as "f".
According to the problem, three years ago, the father was three times as old as his son. So, we can write the equation:
(f - 3) = 3(s - 3)
Next, in five years time, the father will be twice as old as his son. So, we can write the equation:
(f + 5) = 2(s + 5)
We now have a system of two equations with two variables. We can solve these equations to find the current ages of the father and son.
From the first equation, we can simplify it to:
f - 3 = 3s - 9
f = 3s - 9 + 3
f = 3s - 6
Now we substitute this expression for "f" into the second equation:
(3s - 6) + 5 = 2(s + 5)
3s - 1 = 2s + 10
3s - 2s = 10 + 1
s = 11
By substituting the value of "s" back into the first equation, we can find the father's current age:
f = 3(11) - 6
f = 33 - 6
f = 27
So, currently, the son is 11 years old and the father is 27 years old.
To find the sum of their ages in four years time, we need to add 4 to each of their ages:
Son's age in four years: 11 + 4 = 15
Father's age in four years: 27 + 4 = 31
The sum of their ages in four years will be: 15 + 31 = 46.
To solve this problem, let's break it down into steps.
Step 1: Set up equations
Let's assume the current age of the son is S and the current age of the father is F.
Three years ago, the father was three times as old as his son, so we can write the equation:
F - 3 = 3(S - 3)
In five years time, the father will be twice as old as his son, so we can write the equation:
F + 5 = 2(S + 5)
Step 2: Solve the equations
Let's solve the first equation for F:
F - 3 = 3S - 9
F = 3S - 6
Now substitute this value of F into the second equation:
3S - 6 + 5 = 2(S + 5)
3S - 1 = 2S + 10
S = 11
Substitute S = 11 into the first equation to find F:
F = 3(11) - 6
F = 33 - 6
F = 27
So, the current ages of the son and the father are 11 and 27, respectively.
Step 3: Calculate the sum of their ages in four years time
In four years time, the son will be 11 + 4 = 15 years old, and the father will be 27 + 4 = 31 years old.
The sum of their ages in four years time is 15 + 31 = 46.
Therefore, the sum of their ages in four years time is 46.