use systems of equations
the two systems are:
1. expand 6(s+3) to get 6s+18
2. substitute f in terms of s (and we know that f=9s, so then the second equation becomes 9s+3=6s+18
3. now we know how to solve. add -6s to both sides, add -3 to both sides, and finally divide both sides by 3.
so the son is 5 years old and the father is 45 years old
this case is the range of numbers choose sides of a triangle.
so 6 choose 3 = 20
and we want to choose a set of numbers that when you apply the pythagorean theorem (a^2+b^2+c^2) the result is a whole number
only 3, 4, and 5 works in this case between the range 1 to 6 (proof: 3^2+4^2=9+16=25, 25=5^2)
so 1, 2, and 6 doesn't work
so the probablility is 1/2 if no number can be used more than once.
but if a number can be used more than once in the range 1 to 6 (still only the set 3, 4, and 5 works), then the answer is 1/6 choose 3 = 1/20