Pess Persevere with Probloms Determine whether the cost for orderini multiple ltems that will be delivered is sometimes, always, or never proportional. Explain your reasoning.

When determining whether the cost for ordering multiple items that will be delivered is **sometimes**, **always**, or **never** proportional, the most accurate answer is **sometimes proportional**. Here's why: ### **Understanding Proportionality** - **Proportional Cost:** A relationship where the total cost increases linearly with the number of items. For example, if each item costs $10 and there's no additional fee, buying 2 items would cost $20, 3 items $30, and so on. ### **Factors Influencing Proportionality** 1. **Per-Item Pricing:** - **Proportional Scenario:** If each item has a fixed cost and there are no additional fees, the total cost remains proportional to the number of items. For example, buying 5 books at $15 each would cost $75. 2. **Shipping and Handling Fees:** - **Non-Proportional Scenario:** Often, delivery services charge a flat shipping fee regardless of the number of items. For instance, whether you order 1 or 10 items, you might pay a $5 shipping fee. In this case, the total cost doesn’t strictly increase proportionally with each additional item. 3. **Bulk Discounts:** - **Non-Proportional Scenario:** Many retailers offer discounts when purchasing items in larger quantities. For example, buying 10 shirts might cost less per shirt than buying just one, disrupting the proportional relationship. 4. **Tiered Pricing Structures:** - **Sometimes Proportional:** Some businesses use tiered pricing where the cost per item changes based on the quantity ordered. Up to a certain number, the cost is proportional, but beyond that, discounts or increased fees can alter the relationship. 5. **Promotions and Coupons:** - **Non-Proportional Scenario:** Limited-time offers or coupons might reduce the cost for specific quantities, making the overall cost less than what would be expected if purely proportional. ### **Conclusion** The total cost of ordering multiple items for delivery is **sometimes proportional** to the number of items ordered. This proportionality holds true primarily when each item's cost is fixed and there are no additional fees or discounts involved. However, in real-world scenarios, factors like shipping fees, bulk discounts, and promotional pricing often introduce complexities that make the relationship between total cost and quantity non-proportional. Understanding these nuances is essential for accurately predicting costs and making informed purchasing decisions.