A rare coin collection initially has a ratio of gold to non-gold coins equal to 1:3. After adding 10 more gold coins, the ratio becomes 1:2. What is the total number of coins in the collection after the addition?

Introduction / Context:Ratio problems often require translating a verbal description into algebraic relationships. When a quantity changes and a new ratio is specified, you can set up an equation to solve for the original numbers, then recompute the updated totals.

Given Data / Assumptions:

• Initial ratio gold : non-gold = 1 : 3.
• 10 gold coins are added.
• New ratio becomes 1 : 2 (gold : non-gold).

Concept / Approach:Let initial gold coins = g; then non-gold = 3g. After adding 10 gold coins, the new ratio is (g + 10) : 3g = 1 : 2. Solve for g, then compute the final total after addition.

Step-by-Step Solution:

Verification / Alternative check:New gold = 20 + 10 = 30; non-gold = 60. Ratio = 30 : 60 = 1 : 2, consistent with the condition.

Why Other Options Are Wrong:

• 80, 60, 50, 70: These do not match the updated ratio when the 10 gold coins are added and checked against non-gold counts.

Common Pitfalls:

• Interpreting “1:2” as non-gold : gold instead of gold : non-gold.
• Forgetting to add 10 only to gold coins, not to both categories.

Final Answer:90