How to multiply tuples and how to change a format of summation?

General Usage
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1

If you have a set A = [ (1,4,7), (2,5,3), (5,4,9), (2,8,7), (8,6,7), (2,3,5) ] .Is it possible to derive:

#1 another set A'  such that A' = 1.2*A  
each element of A' is the scaled version of A 

#2  define a variable like x and a summation like the following
 
x[1,4,7] + x[2,5,3]+ x[5,4,9]+x[2,8,7]+x[8,6,7]+x[2,3,5] = 5
# not like the following
x[(1,4,7)] + x[(2,5,3)]+ x[(5,4,9)]+x[(2,8,7)]+x[(8,6,7)]+x[(2,3,5)] = 5

The only thing operator I know for this case is ... but this is not useful either.

3 
#with ...
formsum(A,x :: Array{T,2}) where T<: Number =sum([x*[t...] for t in A])


#without ...
formsumf(A,x :: Array{T,2}) where T<: Number = sum(x*Base.splat(hcat)(Base.BroadcastFunction(Base.splat(Base.vect))(A)))
4

It looks like CartesianIndex might be useful to you.

sum(z->x[CartesianIndex(z)], A)

To save a step (or rather to do it earlier), you could make A an array of CartesianIndex{3} rather than 3-tuples.

As for question #1, it’s not pretty but if you want to multiply every element of A every tuple by a constant you can use nested broadcasting with carefully placed dots (although it isn’t pretty):
(.*).(A, 1.2)
Note that this won’t work if you make A an array of CartesianIndex like I’d suggested above, at least not for float factors like your 1.2 since CartesianIndex only supports integers.

Also, don’t be afraid to write for loops in Julia if you can’t figure out how to write something using fancy functions. They aren’t performance traps like in some other languages.