An alloy weighs 50 g and contains 80% gold. How many grams of pure gold must be added so that the new alloy is 90% gold?

Introduction / Context: Alloy-percentage adjustment problems conserve the existing quantity of gold while adding pure gold. Set up the target percentage equation based on the new total weight and new gold amount.

Given Data / Assumptions:

• Initial alloy weight = 50 g.
• Initial gold = 80% of 50 = 40 g.
• Add x g of pure gold; no silver added or removed.
• Target gold% = 90% of (50 + x).

Concept / Approach: Form equation: (40 + x) / (50 + x) = 0.90. Solve for x.

Step-by-Step Solution:

Verification / Alternative check: New total = 100 g; new gold = 90 g ⇒ 90% gold, consistent.

Why Other Options Are Wrong: 60 g would overshoot to 100 * (40+60)/110 ≈ 90.9%; 30 g or 40 g yield 70/80% respectively, not 90%.

Common Pitfalls: Forgetting that only pure gold is added (the silver amount remains 10 g), so the denominator changes along with the numerator.

Final Answer: 50g