The sum of three numbers is 132. The first number is twice the second, and the third number is one-third of the first. Find the value of the second number.

Introduction / Context:This is a classic system-of-equations problem stated in words. By expressing each relationship algebraically and using the total sum, we can solve for the second number directly and check consistency afterward.

Given Data / Assumptions:

• Let the numbers be A (first), B (second), and C (third).
• A + B + C = 132.
• A = 2B.
• C = (1/3) * A.

Concept / Approach:Reduce to a single variable. Replace A with 2B and C with A/3 = (2B)/3 in the sum. Solve for B. Then back-substitute to verify each relation and the overall sum.

Step-by-Step Solution:

Verification / Alternative check:Compute A = 2B = 72 and C = A/3 = 24. Check sum: 72 + 36 + 24 = 132; all conditions hold.

Why Other Options Are Wrong:32, 48, and 60 contradict the equation (11/3)B = 132. 24 is actually the value of C, not B.

Common Pitfalls:Misplacing the one-third relation (e.g., taking C = 3A) or adding coefficients incorrectly when combining fractional terms.

Final Answer:36