Grace can purchase pencils for n dollars per 100 for the first 1500 pencils and 0.5 dollars per 100 thereafter. Which of the following represents the purchase price in dollars for 2500 pencils?

Rationale

20n represents the purchase price in dollars for 2500 pencils.

To calculate the total cost for 2500 pencils, we first find the cost for the first 1500 pencils at n dollars per 100, and then the cost for the remaining 1000 pencils at 0.5 dollars per 100. This gives us a total of 20n dollars.

A (10n) YOUR ANSWER

This option suggests that the total price is only 10n dollars, which would imply that the cost for 2500 pencils is significantly lower than the actual calculation. The first 1500 pencils cost n dollars per 100, totaling 15n dollars, leaving no room for the additional 1000 pencils, making this option incorrect.

B (15n) YOUR ANSWER

While this option correctly represents the cost of the first 1500 pencils at n dollars per 100 (which is indeed 15n), it fails to account for the additional 1000 pencils, which are purchased at a lower rate of 0.5 dollars per 100. Therefore, it does not represent the total cost for 2500 pencils.

C (20n) CORRECT

This is the correct option because it includes both components of the purchase: the cost for the first 1500 pencils (15n) and the cost for the next 1000 pencils (5n), totaling 20n dollars. This captures the entirety of the purchase for 2500 pencils accurately.

D (30n) YOUR ANSWER

This option implies an exaggerated total cost of 30n dollars, which does not correspond to any valid calculation based on the pricing structure given in the question. The cost of the pencils does not add up to this amount, making it incorrect.

Conclusion

The total purchase price for 2500 pencils can be accurately calculated by summing the cost of the first 1500 pencils and the cost of the additional 1000 pencils. The resulting formula yields 20n dollars, reflecting the combination of both pricing tiers. Understanding how to appropriately assess costs in tiers is essential for making accurate financial calculations in similar scenarios.

Grace can purchase pencils for n dollars per 100 for the first 1500 pencils and 0.5 dollars per 100 thereafter. Which of the following represents the purchase price in dollars for 2500 pencils?

20n represents the purchase price in dollars for 2500 pencils.

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