Linked triples: The average of three numbers is 42. The first is twice the second and the second is twice the third. What is the difference between the largest and the smallest number?

Introduction / Context:Ratio chaining across three numbers allows expressing all in one variable. With the average known, compute each and then the required difference (range).Given Data / Assumptions:

• Average of three = 42 ⇒ sum = 126.
• First = 2 * second; Second = 2 * third.

Concept / Approach:Let third = t ⇒ second = 2t ⇒ first = 4t. Then 4t + 2t + t = 7t = 126, so t = 18. Largest is 4t, smallest is t.Step-by-Step Solution:

Verification / Alternative check:Average check: (72 + 36 + 18) / 3 = 126/3 = 42, consistent.Why Other Options Are Wrong:

• 18 and 36: Intermediate values from the ratio, not the range.
• 72: Largest value itself, not the difference.

Common Pitfalls:Reversing the doubling chain or forgetting that average fixes the sum first.Final Answer: