Five numbers have an average of 72. The first number equals one-eighth of the sum of the other four numbers. What is the value of the first number?

Introduction: Averages convert to totals cleanly. If one number is a stated fraction of the sum of the others, set up an equation in terms of the sum of the remaining numbers and solve for the first number directly.

Given Data / Assumptions: Average of 5 numbers = 72 ⇒ total T = 5 * 72 = 360. Let S = sum of the other four numbers. First number = (1/8) * S.

Concept / Approach: Total T = first + S = (1/8)S + S = (9/8)S. Solve for S from T, then compute first = S / 8.

Step-by-Step Solution: (9/8) * S = 360 ⇒ S = 360 * (8/9) = 320. First number = S / 8 = 320 / 8 = 40.

Verification / Alternative check: Check totals: First = 40, others sum to 320, total = 360, average = 360 / 5 = 72, consistent with the given average.

Why Other Options Are Wrong: 60, 26, 80, 32: None satisfy the relation first = (1/8) of the sum of the other four with total 360.

Common Pitfalls: Adding 1/8 directly to the average or misinterpreting “one-eighth of the sum of other four” as one-eighth of the total. Always define variables clearly and use totals.

Final Answer: The first number is 40.