The sum of a non-zero number and four times its reciprocal is 17/2. What is that number?

Introduction / Context:
This problem involves a number and its reciprocal. Questions like this test algebraic manipulation skills and understanding of how a number interacts with its reciprocal, which is common in equations and ratio problems.

Given Data / Assumptions:

• Let the non-zero number be x.
• The reciprocal of x is 1/x.
• We are told that x + 4 * (1/x) = 17/2.
• We must find the value of x from the given options.

Concept / Approach:
We translate the given verbal condition into an algebraic equation, then clear the denominator and solve the resulting quadratic equation. Finally, we check which solution matches the options.

Step-by-Step Solution:

Verification / Alternative check:
Check x = 8: 8 + 4 * (1/8) = 8 + 1/2 = 8.5 = 17/2, which satisfies the equation. Check x = 1/2: 1/2 + 4 * 2 = 1/2 + 8 = 8.5 = 17/2, which also satisfies the equation. Both numbers are mathematically valid, but only 8 appears among the given options.

Why Other Options Are Wrong:
Substituting x = 12, 16 or 4 into x + 4/x does not yield 17/2. For example, with x = 4 we get 4 + 4 * (1/4) = 5, not 17/2. Therefore these choices do not satisfy the condition.

Common Pitfalls:
A typical mistake is forgetting to multiply every term by the common denominator 2x, or solving the quadratic incorrectly. Another pitfall is assuming only one solution must exist, without checking which one matches the multiple choice options.

Final Answer:
The value of the number that satisfies the condition and matches the options is 8.