Number and Its Reciprocal — Translate to a Quadratic A positive number, when increased by 10, equals 200 times its reciprocal. What is the number?

Introduction / Context:
Problems linking a number to its reciprocal typically lead to a quadratic equation. This question tests your ability to convert a verbal condition into algebra and then solve efficiently while keeping track of the positivity constraint.

Given Data / Assumptions:

• N is a positive real number.
• N + 10 = 200 * (1/N).
• We must determine N.

Concept / Approach:
Multiplying through by N removes the reciprocal and yields a standard quadratic in N. Solve via the quadratic formula or factoring (after computing the discriminant). Discard any negative root because the problem specifies a positive number.

Step-by-Step Solution:
Start with N + 10 = 200/N.Multiply both sides by N: N^2 + 10N = 200.Rearrange: N^2 + 10N − 200 = 0.Discriminant: 10^2 + 4*200 = 100 + 800 = 900; sqrt = 30.Roots: N = (−10 ± 30)/2 → N = 10 or N = −20. Take the positive root N = 10.

Verification / Alternative check:
Check N = 10: left side 10 + 10 = 20; right side 200 * (1/10) = 20. The equality holds.

Why Other Options Are Wrong:
100, 20, and 200 do not satisfy the equation; 5 also fails since 5 + 10 = 15 while 200*(1/5) = 40.

Common Pitfalls:
Forgetting to multiply through by N; mishandling signs when applying the quadratic formula; accidentally keeping the negative root even though the number must be positive.

Final Answer:
10