Three-number relation and average: The first number is twice the second and half of the third. If the average of the three numbers is 56, find the ordered triple (first, second, third).

Introduction / Context:
This problem blends proportional relationships with an average constraint. Setting variables based on the relationships simplifies solving the system.

Given Data / Assumptions:

• First = twice the second
• First = half of the third
• Average of three numbers = 56

Concept / Approach:
Let the second be x. Then first = 2x and third = 4x. Use the average to find x and build the ordered triple.

Step-by-Step Solution:

Verification / Alternative check:
Check relations: 48 is twice 24 and half of 96. Average = (48 + 24 + 96) / 3 = 168 / 3 = 56, correct.

Why Other Options Are Wrong:

• All other permutations break at least one relation or do not average to 56.

Common Pitfalls:
Assigning inconsistent variables (e.g., mixing up which is half or double) or forgetting to apply average to three numbers.

Final Answer:
48, 24, 96