A company buys paper clips at the rate of $7.50 per box for the first 10 boxes, $5.50 per box for the next 10 boxes, and $3.50 per box for any additional boxes. How many boxes of paper clips can be bought for $221.00?
The correct answer and explanation is:
To determine how many boxes of paper clips a company can buy for $221.00, we break the purchase into three pricing tiers:
- First 10 boxes: $7.50 per box
- Cost: 10×7.50=75.0010 \times 7.50 = 75.00
- Remaining budget: 221.00−75.00=146.00221.00 – 75.00 = 146.00
- Next 10 boxes: $5.50 per box
- Cost: 10×5.50=55.0010 \times 5.50 = 55.00
- Remaining budget: 146.00−55.00=91.00146.00 – 55.00 = 91.00
- Additional boxes: $3.50 per box
- Number of boxes that can be bought:
91.00÷3.50=2691.00 \div 3.50 = 26 boxes
- Number of boxes that can be bought:
Total boxes purchased:
- 10 (first tier)
- 10 (second tier)
- 26 (third tier)
- Total: 46 boxes
Explanation:
The company purchases paper clips in bulk with a tiered pricing system. The pricing structure benefits bulk buying, as the cost per box decreases for larger purchases.
First, the company spends $75.00 to buy 10 boxes at the highest price of $7.50 each. The remaining budget is then used to buy 10 more boxes at a reduced rate of $5.50 each, costing an additional $55.00. With $91.00 left, the company takes advantage of the lowest price tier of $3.50 per box, allowing them to buy 26 more boxes.
By calculating sequentially and ensuring that the total cost does not exceed $221.00, we determine that the company can buy 46 boxes in total.
Now, I will generate an image representing this calculation visually.
Here is the infographic illustrating the tiered pricing and purchase breakdown of paper clips. Let me know if you need any modifications or further explanations!