Laptops Purchase Problem

Problem Statement

  • A school has received a donation of $20,000 for the purchase of new laptops.
  • Each laptop costs $149.
  • No tax is charged on the laptops.
  • The manufacturer offers a 7.5% discount on orders of at least 100 laptops.
  • Objective: Determine the maximum number of laptops the school can purchase with the donation.

Key Values

  • Total Donation: $20,000
  • Cost Per Laptop: $149
  • Discount Rate: 7.5% (applicable for orders of at least 100 laptops)

Calculation Steps

  1. Determine the discount price per laptop:

    • If the school orders 100 laptops or more, the discount applies.
    • Calculate the discount:
      • Discount = Cost Per Laptop × Discount Rate
      • Discount = $149 × 0.075 = $11.175
    • Price after discount = Cost Per Laptop - Discount
      • Price after discount = $149 - $11.175 = $137.825

  2. Calculate the maximum number of laptops without discount:

    • Maximum laptops (no discount) = Total Donation / Cost Per Laptop
    • Maximum laptops = $20,000 / $149 ≈ 134.225
    • The maximum whole number of laptops without the discount is 134.

  3. Calculate the maximum number of laptops with discount:

    • Maximum laptops (with discount) = Total Donation / Price after discount
    • Maximum laptops = $20,000 / $137.825 ≈ 145.00
    • Hence, the maximum whole number of laptops that can be purchased with the discount is 145.

Conclusions

  • The maximum number of laptops that the school can purchase with the $20,000 donation, considering the 7.5% discount for orders of at least 100 laptops, is 145 laptops.

Answer Choices

  • A. 124
  • B. 134
  • C. 145
  • D. 146
  • Correct Answer: C. 145