Final answer:
In a scenario where Z gets N, Y gets N/2, and X gets N/4, and Z's share is 26 out of a total of 68, Y's share would be 13.
Step-by-step explanation:
The problem states that for every N, which we will call the base value, that Z gets, Y gets N/2, and X gets N/4. We can use this information to establish a ratio of their shares: X : Y : Z = N/4 : N/2 : N which simplifies to 1 : 2 : 4. If Z gets 26 (since we use Z = 26 to get there), then the total N must be 68, because the question defines the total amount shared as N68. To determine Y's share, we consider the ratio, where Y gets 2 parts for every 4 parts Z gets. Z's share of 26 corresponds to 4 parts in the ratio, which implies each part is worth 26 / 4 = 6.5. Since Y gets 2 parts, Y's share is 2 * 6.5 = 13.