A father is 7 times as old as his son. Three years ago, the father was 13 times as old as his son. What are their present ages?

To solve this problem, we need to set up equations based on the information given.
Let's define:

f as the father's current age.

s as the son's current age.


Step 1: Create equations based on the problem statement

According to the problem, the father is 7 times as old as his son: f = 7 s

Three years ago, the father was 13 times as old as his son. Three years ago, the father's age would have been f − 3 , and the son's age would have been s − 3 . Thus, we can write: f − 3 = 13 ( s − 3 )


Step 2: Simplify the equations

From equation 1, we already have f = 7 s .

Substitute f = 7 s into the second equation: 7 s − 3 = 13 ( s − 3 )


Step 3: Solve for s

Expand the right side of the equation: 7 s − 3 = 13 s − 39

Bring like terms together: 7 s − 13 s = − 39 + 3

Simplify: − 6 s = − 36

Divide both sides by − 6 :
s = 6


So, the son is currently 6 years old.
Step 4: Solve for f

Substitute s = 6 back into equation 1: f = 7 × 6 = 42

So, the father is currently 42 years old.
Conclusion
The present ages are:

Son: 6 years old

Father: 42 years old

Answered by ElijahBenjaminCarter | 2025-07-22