Consecutive multiples of 3, fixed sum: The sum of three consecutive multiples of 3 is 72. What is the largest of these three numbers?

Introduction / Context:Consecutive multiples introduce a constant step equal to the base multiple. Represent the three numbers with a single parameter and solve the linear sum equation to recover the sequence.

Given Data / Assumptions:

• Let the numbers be 3k, 3k + 3, 3k + 6
• Sum = 72

Concept / Approach:Set up the sum: 9k + 9 = 72. Solve for k, then compute the largest term (3k + 6).

Step-by-Step Solution:9k + 9 = 72 → 9k = 63 → k = 7Numbers: 21, 24, 27; largest = 27

Verification / Alternative check:The sum 21 + 24 + 27 = 72 confirms the calculation.

Why Other Options Are Wrong:21 and 24 are smaller members of the set; 36 and 30 are not consistent with the given sum for consecutive triples.

Common Pitfalls:Using 3k, 3k + 1, 3k + 2 instead of the correct step size of 3 for multiples of 3.

Final Answer:27