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).
Aptitude
Average
Difficulty: Medium
Choose an option
Answer
Correct Answer: 48, 24, 96
Explanation
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:
Numbers: 2x, x, 4xAverage = (2x + x + 4x) / 3 = 7x / 3Set 7x / 3 = 56, so 7x = 168, x = 24First = 48, Second = 24, Third = 96Verification / 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