An ore contains 12% copper. How many kilograms of ore are needed to extract 69 kg of pure copper?

Introduction / Context:
Percentage composition problems convert a desired pure quantity into the amount of mixture required. If ore has 12% copper, 12 parts out of 100 are copper. We scale up to obtain 69 kg of copper.

Given Data / Assumptions:

• Ore copper content = 12% by mass.
• Required copper (pure) = 69 kg.

Concept / Approach:
Let the ore mass be M kg. Then copper from ore = 0.12M. Set 0.12M = 69 → M = 69 / 0.12. Working with fractions (12% = 12/100 = 3/25) speeds up the arithmetic: 69 ÷ (3/25) = 69 * (25/3).

Step-by-Step Solution:

Verification / Alternative check:
Check: 12% of 575 = 0.12 * 575 = 69 exactly.

Why Other Options Are Wrong:

• 424, 828, 1736 2/3: These do not give 69 kg of copper at 12% concentration when tested.

Common Pitfalls:
Multiplying by 0.12 instead of dividing by it when recovering the whole from a part, or misreading 12% as 1/12.

Final Answer: