If the father's age in 3 years will be twice the son's age 4 years ago, and if the sum of their ages now is 106, how old is the father now?
67
The correct answer is 67.
Here's how to solve it:
Let's use f for the father's age and s for the son's age.
From the first condition:
f + 3 = 2(s-4)
Simplifying this:
f + 3 = 2s - 8
f = 2s - 11
From the second condition:
f + s = 106
Substitute the first equation into the second:
(2s - 11) + s = 106
3s - 11 = 106
3s = 117
s = 39
Now we can use either of the two equations to find f:
f + 39 = 106
f = 67
So the father is currently 67 years old.
To find the age of the father now, we can set up a system of equations based on the given information.
Let's assume:
- The father's current age is represented by F.
- The son's current age is represented by S.
We are given two conditions:
1. "If the father's age in 3 years will be twice the son's age 4 years ago": This can be written as
F + 3 = 2(S - 4)
2. "The sum of their ages now is 106": This can be written as
F + S = 106
We can solve these two equations simultaneously to find the values of F and S.
Let's start by solving equation 1 for F:
F + 3 = 2(S - 4)
F + 3 = 2S - 8
F = 2S - 8 - 3
F = 2S - 11
Now substitute this value of F into equation 2:
(2S - 11) + S = 106
3S - 11 = 106
3S = 106 + 11
3S = 117
S = 117 / 3
S = 39
Now that we know S (son's age is 39), we can substitute this value back into equation 2 to find F (father's age):
F + 39 = 106
F = 106 - 39
F = 67
Therefore, the father's age now is 67 years.
f+s = 106
f+3 = 2(s-4)
now crank it out.