17. Of the coins in a certain collection, 30 percent were issued more than ten years ago and 45 percent are foreign. Of the foreign coins, 20 percent were issued more than ten years ago. If there are 1,500 coins in the collection, how many are foreign coins that were issued ten years ago or less?
Answer: E
There are 540 foreign coins that were issued ten years ago or less.
To determine how many foreign coins were issued ten years ago or less, we first calculate the total number of foreign coins in the collection, which is 45% of 1,500, equaling 675 coins. From the foreign coins, 20% were issued more than ten years ago, which translates to 135 coins. Therefore, the number of foreign coins issued ten years ago or less is 675 - 135 = 540.
A) 75
This option is incorrect because it underestimates the number of foreign coins issued ten years ago or less. Based on the calculations, this number is significantly higher than 75, as it does not account for the total number of foreign coins or the correct percentage issued over ten years ago.
B) 135
This option represents the number of foreign coins that were issued more than ten years ago, not those issued ten years ago or less. Thus, it is not a valid answer to the question being asked regarding the total number of foreign coins in the specified age range.
C) 315
This option is incorrect because it does not reflect the correct calculation for the number of foreign coins issued ten years ago or less. The actual number, as calculated, is 540, making 315 insufficient and inaccurate in relation to the data provided.
D) 375
This option is incorrect as it also fails to represent the accurate calculation of foreign coins issued ten years ago or less. The correct figure, as determined, is 540, which is much higher than 375, thus making this option invalid.
E) 540
This option is correct as it accurately represents the number of foreign coins that were issued ten years ago or less. After calculating the total number of foreign coins and subtracting those issued more than ten years ago, we arrive at this figure.
Conclusion
The correct answer is 540 foreign coins issued ten years ago or less, as it follows directly from the calculations based on the percentages provided. All other options fail due to their inaccurate representation of the total foreign coins or misinterpretation of the time frame in question.