Of three numbers whose average is 40, the first number is one third of the sum of the other two. What is the value of the first number?

Introduction / Context:
This question combines averages with simple algebraic relationships between three numbers. It checks whether the student can translate a verbal condition into equations and then use the given average to solve for specific values.

Given Data / Assumptions:
- There are three numbers: call them A, B, and C.
- The average of A, B, and C is 40, so (A + B + C) ÷ 3 = 40.
- The first number A is one third of the sum of the other two, so A = (B + C) ÷ 3.
- We must find the value of A.

Concept / Approach:
From the average, we obtain the total sum of the three numbers. From the relationship involving the first number, we obtain another equation connecting A, B, and C. Combining these two equations allows us to express everything in terms of A and solve for it.

Step-by-Step Solution:
From the average: (A + B + C) ÷ 3 = 40, so A + B + C = 120. From the given condition: A = (B + C) ÷ 3, so B + C = 3A. Substitute B + C = 3A into the sum: A + (B + C) = A + 3A = 4A. We know A + B + C = 120, so 4A = 120. Therefore A = 120 ÷ 4 = 30.

Verification / Alternative Check:
If A = 30, then B + C = 3A = 90. The total sum A + B + C is 30 + 90 = 120. Dividing by 3 gives an average of 40, which matches the given average. Also, A is indeed one third of B + C, since 30 = 90 ÷ 3. Both conditions are satisfied, confirming the solution.

Why Other Options Are Wrong:
If A were 20, then B + C would be 60, making the total 80, whose average is 80 ÷ 3, not 40.
If A were 50, then B + C would be 150, total 200, whose average is greater than 40.
If A were 25, then B + C would be 75 and the average would not be 40.
If A were 40, then the total 4A would be 160, giving an average of 160 ÷ 3, not 40.

Common Pitfalls:
Learners sometimes mix up which number is one third of the sum of the other two and may incorrectly write B = (A + C) ÷ 3 or a similar expression. Others forget to use the average to find the total sum first, which makes solving the system harder than necessary. Writing the equations step by step keeps the algebra simple and clear.

Final Answer:
The first number is 30.