I am not sure if you gave all of the information but if you did A because A > B. Did I miss something?
T=2A+4
S=5A-8
If Tom and Sara are 10 years old,
10=2A+4
6=2A
3=A
Not sure though
1/2 (14x-2)-1/4(4x-24) = 6x + 5
has ten elements, so any proper subset has at most nine of these elements.
The number of ways of taking any
letters from this set is given by the binomial coefficient,
and in particular, the total number of ways to picking proper subsets is
Without computing each term directly, let's instead use a direct result from the binomial theorem, which says
If we replace
, then we're left with
We can use this to evaluate our sum directly: