The sum of three consecutive multiples of 3 is 72. What is the second largest of these three numbers?

Introduction / Context:
This question involves consecutive multiples of 3 and their sum. You are told that the sum of three such consecutive multiples equals 72 and are asked to find the second largest number. It is a straightforward algebra problem that helps you practise forming and solving simple equations with consecutive terms.

Given Data / Assumptions:

• The three numbers are consecutive multiples of 3.
• Their total sum is 72.
• We must find the second largest number among these three.
• We assume positive integers and standard arithmetic operations.

Concept / Approach:
If the smallest of the three consecutive multiples is 3n, then the next two are 3n + 3 and 3n + 6. The sum of these three numbers is given, so we can express that sum in terms of n, set it equal to 72, and solve for n. Once we know n, we can write down each multiple and identify the second largest number among them.

Step-by-Step Solution:
Step 1: Let the three consecutive multiples of 3 be 3n, 3n + 3, and 3n + 6.Step 2: Their sum is 3n + (3n + 3) + (3n + 6).Step 3: Simplify this sum: 3n + 3n + 3 + 3n + 6 = 9n + 9.Step 4: According to the problem, 9n + 9 = 72.Step 5: Subtract 9 from both sides: 9n = 63.Step 6: Divide both sides by 9: n = 7.Step 7: The three numbers become 3*7 = 21, 3*7 + 3 = 24, and 3*7 + 6 = 27.Step 8: The second largest number is the middle one, which is 24.

Verification / Alternative check:
We can quickly verify the numbers: 21, 24, and 27 are indeed multiples of 3 and consecutive in that progression. Their sum is 21 + 24 + 27 = 72, which matches the problem statement. Among these, the largest number is 27, the second largest is 24, and the smallest is 21. Therefore, 24 is confirmed as the correct answer.

Why Other Options Are Wrong:
Option A (27): This is the largest number, not the second largest.
Option C (21): This is the smallest of the three numbers.
Option D (42): This number does not appear in the set of three consecutive multiples whose sum is 72.

Common Pitfalls:
One common mistake is to interpret “consecutive multiples of 3” as consecutive integers or to miswrite them as 3n, 3n + 1, 3n + 2. Another error is to forget that the second largest of three ordered numbers is simply the middle one. Carefully setting up the expression with 3n, 3n + 3, and 3n + 6 prevents such confusion.

Final Answer:
The three consecutive multiples of 3 are 21, 24, and 27, so the second largest number is 24.