Nested relations with a total: X is four years older than Y, and Y is twice as old as Z. If X + Y + Z = 34, how old is X?

Introduction / Context:Express all ages in terms of Z, use the total to solve Z, then recover X. This is a standard linear reduction technique.

Given Data / Assumptions:

• Y = 2Z.
• X = Y + 4 = 2Z + 4.
• (2Z + 4) + 2Z + Z = 34.

Concept / Approach:Collapse to a single variable Z; compute backwards to X.

Step-by-Step Solution:1) 5Z + 4 = 34 ⇒ 5Z = 30 ⇒ Z = 6.2) Y = 12; X = 16.

Verification / Alternative check:Sum check: 16 + 12 + 6 = 34; difference check: X − Y = 4; Y = 2Z. All consistent.

Why Other Options Are Wrong:They fail either the total or one of the given relations.

Common Pitfalls:Arithmetic slips adding three terms, or forgetting the +4 offset for X.

Final Answer:16