x/y = 3/4 ---> 4x = 3y (cross-multiplying)
y/z = 2/3 ---> 3y = 2z
z/w = 5/8 ---> 8z = 5w
What is (x + y + w) / w?
Notice that there is no z is the question.
This means that we should rewrite each of the variables in the question in terms of z; then all the z-terms will cancel out.
Since 8z = 5w ---> w = (8/5)z
Since 3y = 2z ---> y = (2/3)z
Since 4x = 3y and 3y = 2z, 4x = 2z ---> x = (1/2)z
(x + y + w) / w ---> [ (1/2)z + (2/3)z + (8/5)z ] / [ (8/5)z ]
The z's will cancel ---> [ 1/2 + 2/3 + 8/5 ] / [ 8/5 ]
---> 83/30 / 8/5
---> 83 / 48