Four numbers have an average of 60. The first number is one fourth of the sum of the last three numbers. What is the value of the first number?

Introduction / Context:
This question tests your understanding of averages and simple algebraic relationships between numbers. You are told that the average of four numbers is known, and that the first number is one fourth of the sum of the remaining three. Using these conditions, you must determine the value of the first number. Such problems reinforce the link between averages, totals and linear equations.

Given Data / Assumptions:
- There are four numbers: let them be a, b, c and d.
- Average of the four numbers = 60.
- Therefore, total sum of the four numbers = 4 * 60 = 240.
- The first number a is one fourth of the sum of the last three numbers b, c and d.
- So a = (1 / 4) * (b + c + d).

Concept / Approach:
From the average, we know the total sum of all four numbers. The condition relating a to the sum of b, c, and d can be combined with this total to form an equation involving a only. After that, solving the equation gives us the exact value of the first number. This is a straightforward application of algebra with averages.

Step-by-Step Solution:
Step 1: Total sum of all four numbers = a + b + c + d = 240.Step 2: From the given condition, a = (1 / 4) * (b + c + d).Step 3: Note that b + c + d = 240 - a.Step 4: Substitute into the relation a = (1 / 4) * (b + c + d) to get a = (1 / 4) * (240 - a).Step 5: Multiply both sides by 4: 4a = 240 - a.Step 6: Bring terms together: 4a + a = 240, so 5a = 240.Step 7: Therefore a = 240 / 5 = 48.

Verification / Alternative Check:
If a = 48, then b + c + d = 240 - 48 = 192. One fourth of 192 is 48, which matches a. Thus the condition is exactly satisfied. Also, the average becomes (48 + 192) / 4 = 240 / 4 = 60, which matches the given average. So 48 is consistent with all information in the question.

Why Other Options Are Wrong:
Values like 17, 29 or 36 do not satisfy the equation a = (1 / 4) * (240 - a). Substituting any of those options leads to a mismatch between left-hand side and right-hand side. Therefore, they cannot be the correct first number for the given average and relationship.

Common Pitfalls:
Learners sometimes confuse the phrase one fourth of the sum of the last three with one fourth of each of the last three. Another error is to assume that the first number is simply 60, the same as the average. Writing down the equations carefully and using the total sum 240 avoids these misunderstandings.

Final Answer:
The first number is 48.