While it's possible to solve this problem with a lot of algebra, it is better to reason through it by recognizing that k is a constant that illustrates the distances between x, y, and z. Imagine them on a number line, and choose sample numbers to make the problem easier to work with.

If x = 2 and k = 3, then y = x + k = 2 + 3 = 5.

Given that y = 5, y + 3k = 5 + 3(3) = 14, so z = 14.

Thus:

z – x = 14 – 2 = 12

y – x = 5 – 2 = 3

The ratio of 12 to 3 simplifies to 4 to 1, choice (E).

Another way of looking at this is that the distance between y and x (y – x) is one k. The distance between y and z is three k's, so the total distance between x and z is four k's. Thus, z – x is four k's, y – x is one k, meaning the ratio is 4 to 1.