We are given that the relationship between the number of pounds of apples and the total cost is proportional. From the table:

• For 2 pounds of apples, the cost is $4.50.
• For 3 pounds of apples, the cost is $6.75.

To solve this, we first determine the cost per pound by using the proportionality between the two given points.

Step 1: Find the Unit Rate (Cost per Pound)

For 2 pounds costing $4.50: $\text{Cost per pound} = \frac{4.50}{2} = 2.25 \text{ dollars per pound}$

Step 2: Verify the Proportionality

For 3 pounds, the cost is $6.75: $\frac{6.75}{3} = 2.25 \text{ dollars per pound}$ This confirms that the relationship is indeed proportional, as both unit rates are equal.

Step 3: Calculate the Cost for 15 Pounds

Using the unit rate of $2.25 per pound, we calculate the cost for 15 pounds: $\text{Cost for 15 pounds} = 2.25 \times 15 = 33.75 \text{ dollars}$

Therefore, Daniella will spend $33.75 for 15 pounds of apples.

Would you like more details on any step, or do you have any further questions?

Here are five related questions you might explore:

1. What if the cost per pound changed over time? How would we adjust the calculation?
2. How would we graph this proportional relationship between pounds and cost?
3. How can you find the total cost for a different number of pounds, say 10 pounds?
4. What is the algebraic equation representing this situation?
5. Can we apply this method to other proportional relationships in real life, like fuel or groceries?

Tip: When dealing with proportional relationships, always check the unit rate to ensure consistency.