Solving with averages and linear relations: The average of x1, x2, and x3 is 14 (so x1 + x2 + x3 = 42). Twice the sum of x2 and x3 is 30 (i.e., 2 * (x2 + x3) = 30). What is the value of x1?

Introduction / Context:
Averages often give a sum; paired with another relation, we can isolate a specific variable.

Given Data / Assumptions:

• (x1 + x2 + x3) / 3 = 14 → x1 + x2 + x3 = 42
• 2 * (x2 + x3) = 30 → x2 + x3 = 15

Concept / Approach:
Use the two equations to solve for x1 directly by subtracting the sum of x2 and x3 from the total.

Step-by-Step Solution:
x1 + x2 + x3 = 42x2 + x3 = 15x1 = 42 - 15 = 27

Verification / Alternative check:
Check that 2 * (x2 + x3) equals 30 when x1 is 27; since x2 + x3 = 15, this matches the given condition.

Why Other Options Are Wrong:
20, 16, 2, 12 do not satisfy both equations simultaneously.

Common Pitfalls:
Dividing 30 by 2 incorrectly or mixing up which pair is summed; always write both equations first.

Final Answer:
27