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?
Aptitude
Elementary Algebra
Difficulty: Easy
Choose an option
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A90
-
B80
-
C60
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D50
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E70
Answer
Correct Answer: 90
Explanation
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:
(g + 10) / (3g) = 1 / 2Cross-multiply: 2(g + 10) = 3g2g + 20 = 3g ⇒ g = 20Initial total = g + 3g = 4g = 80After adding 10 gold coins: total = 80 + 10 = 90Verification / 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