30. 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?
Answer: C
The purchase price for 2500 pencils is represented by 20n.
To calculate the total purchase price for 2500 pencils, we consider the first 1500 pencils purchased at n dollars per 100 and the remaining 1000 pencils purchased at 0.5 dollars per 100. This results in a total cost of 20n dollars.
A) 10n
This option incorrectly calculates the total cost. At 10n, it would suggest that the total price for 2500 pencils is significantly lower than the actual calculated amount, resulting from the reduced rate for the additional 1000 pencils.
B) 15n
Selecting 15n implies a misunderstanding of the pricing structure. This amount does not account for the full cost of the additional 1000 pencils purchased at the lower rate, leading to an underestimation of the total price.
C) 20n
This option accurately captures the total cost for 2500 pencils. The first 1500 pencils cost 15n (1500/100 * n), and the subsequent 1000 pencils cost 5n (1000/100 * 0.5). The total is therefore 15n + 5n = 20n.
D) 30n
This choice suggests an inflated total cost for the pencils. At 30n, the calculation would imply that the price of the additional 1000 pencils is incorrectly estimated, failing to apply the discounted rate effectively.
Conclusion
The correct option is 20n, as it accurately reflects the cost structure for purchasing 2500 pencils, taking into account both the initial and additional quantities. All other options either underestimate or overestimate the total cost based on the pricing rules provided.