Alloy 1 contains gold and silver in the ratio 5:8 (gold:silver). Alloy 2 contains gold and silver in the ratio 5:3 (gold:silver). If equal amounts of alloy 1 and alloy 2 are melted together, what will be the ratio of gold to silver in the resulting alloy?

Introduction / Context:This problem tests combining alloys by converting ratios into fractions. When equal amounts are combined, you can assume 1 unit from each alloy. Then compute gold and silver contributions from each unit using the ratio fractions, add them, and form the final ratio.

Given Data / Assumptions:

• Alloy 1 gold:silver = 5:8 (total 13 parts)
• Alloy 2 gold:silver = 5:3 (total 8 parts)
• Equal amounts of both alloys are mixed
• Assume 1 kg from each alloy (any equal amount works)

Concept / Approach:Gold fraction in alloy = gold parts / total parts. Silver fraction similarly. Add gold and silver from both equal quantities and simplify.

Step-by-Step Solution:

Verification / Alternative check:The ratio is close to 1:1 because both alloys contain significant gold and silver. Since alloy 2 is richer in gold than alloy 1, the final gold should be slightly higher than silver, which matches 105:103.

Why Other Options Are Wrong:

Common Pitfalls:A typical mistake is to average ratios directly (like averaging 5:8 and 5:3) which is not valid. Another mistake is forgetting that equal amounts are mixed, so you must use fractions and common denominators, not part counts alone.

Final Answer:105:103