In a rare coin collection, there is one gold coin for every three non-gold coins. 10 more gold coins are added to the collection and the ratio of gold coins to non-gold coins would be 1: 2. Based on the information; the total number of coins in the collection now becomes

Let G be the initial number of gold coins and N be the initial number of non-gold coins.

1. From the first statement, "one gold coin for every three non-gold coins": G / N = 1 / 3 This implies N = 3G.

2. From the second statement, "10 more gold coins are added... the ratio of gold coins to non-gold coins would be 1:2": The new number of gold coins is G + 10. The number of non-gold coins remains N. So, (G + 10) / N = 1 / 2

3. Substitute N = 3G (from step 1) into the equation from step 2: (G + 10) / (3G) = 1 / 2

4. Cross-multiply to solve for G: 2 * (G + 10) = 1 * (3G) 2G + 20 = 3G 20 = 3G - 2G G = 20

5. Now that we have G, find N using N = 3G: N = 3 * 20 = 60

6. The question asks for the total number of coins in the collection NOW (after adding 10 gold coins). New number of gold coins = G + 10 = 20 + 10 = 30 Number of non-gold coins = N = 60 Total number of coins NOW = 30 + 60 = 90

Therefore, the total number of coins in the collection now is 90.

Analyzing the options: A) 90: This matches our calculated total number of coins after adding 10 gold coins. B) 80: This would be the initial total number of coins (20 gold + 60 non-gold), not the total after adding more. C) 60: This is the number of non-gold coins. D) 50: This is incorrect.

The final answer is A.