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

The purchase price for 2,500 pencils is represented by 20n.

To determine the total cost for purchasing 2,500 pencils, we calculate the cost for the first 1,500 pencils at the rate of $n per 100 and then for the remaining 1,000 pencils at the rate of $n per 1002. This results in a total purchase price of 20n.

A (10n) YOUR ANSWER

This choice only accounts for the cost of 1,000 pencils at $n per 100, which would be $n × 10 = 10n. However, it completely neglects the cost of the first 1,500 pencils, leading to an incorrect total.

B (15n) YOUR ANSWER

This option incorrectly assumes a cost structure that does not align with the given pricing model. It does not accurately reflect the total cost of both segments of pencils, as it only considers part of the first 1,500 pencils and underestimates the overall cost.

C (20n) CORRECT

This is the correct calculation. The cost for the first 1,500 pencils is 15n (1,500 pencils is 15 sets of 100), and the cost for the additional 1,000 pencils is an additional 5n (10 sets of 100). Therefore, 15n + 5n totals 20n.

D (30n) YOUR ANSWER

This choice mistakenly suggests that the total cost of 2,500 pencils is triple the cost of the first 1,500 pencils, miscalculating the cost associated with the second segment. The pricing structure does not support such a high total.

Conclusion

The total purchase price for 2,500 pencils must account for both tiers of pricing. The correct calculation yields a total price of 20n, combining the cost of 1,500 pencils at the initial price and 1,000 additional pencils at the subsequent rate. This understanding of tiered pricing is crucial for accurate financial planning in bulk purchases.

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?

The purchase price for 2,500 pencils is represented by 20n.

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