Percent-of-a-number equation: The sum of 15% of a positive number and 20% of the same number equals 126. What is one-third of that number?

Introduction / Context:
This question assesses comfort with combining multiple percentages of the same unknown and then extracting a specific fraction (one-third) of the number. It is a straightforward linear equation involving percentages.

Given Data / Assumptions:

• Unknown positive number = N.
• 15% of N plus 20% of N totals 126.
• We need one-third of N.

Concept / Approach:
Combine the percentages first: 15% + 20% = 35% of N. Convert 35% to decimal 0.35 and solve 0.35N = 126. Once N is found, compute N/3 directly.

Step-by-Step Solution:

Verification / Alternative check:
Compute 15% and 20% of 360: 0.15*360 = 54, 0.20*360 = 72, sum = 126. The computation is consistent, so one-third is 120.

Why Other Options Are Wrong:

• 360: That is the full N, not one-third.
• 1080: Triple of N; misreading the request.
• 40: One-ninth of N; incorrect fraction.

Common Pitfalls:
Adding percentages incorrectly (e.g., 15 + 20 = 30), or forgetting to divide by 3 at the end. Carefully track what is being asked: one-third of the number after finding N.

Final Answer: