At present, the sum of the ages of a father and his son is 33 years. Determine the smallest number of years until the father's age is 4 times the son's age.

Answer 1

f+s=33
f+x = 4(s+x)

clearly, f > 4x now, since f/s decreases as both grow
So, f > 24, meaning s < 7

You want f to be close to 4s now, so try

s=6, f=27
In one year, s=7, f=28
Looks like 1 is the smallest value.

Answer 2

Thank you, Steve