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To solve this problem, we need to calculate how much food Amanda and Sydney should order for a party of 40 guests, plus 35 additional drop-in guests, with each drop-in guest counting as half a guest.

### Step 1: Calculate total guest count
- Original guests = 40
- Drop-in guests (each counts as half) = 35 / 2 = 17.5

Total guests = 40 + 17.5 = 57.5 guests.

### Step 2: Determine the proportion for the new number of guests
The table lists the recommended food amounts for 23 guests, so we need to adjust the amounts based on 57.5 guests.

The proportion for 57.5 guests relative to 23 guests is:
\[
\frac{57.5}{23} = 2.5
\]

### Step 3: Multiply the listed amounts of food by the proportion

1. **Fried Chicken**: 28 pieces for 23 guests.
   \[
   28 \times 2.5 = 70 \text{ pieces of chicken}
   \]

2. **Deli Meats**: \(4 \frac{1}{3}\) pounds for 23 guests.
   \[
   4 \frac{1}{3} = \frac{13}{3} \quad \text{so} \quad \frac{13}{3} \times 2.5 = \frac{32.5}{3} = 10 \frac{5}{6} \text{ pounds of deli meats}
   \]

3. **Lasagna**: \(10 \frac{1}{4}\) pounds for 23 guests.
   \[
   10 \frac{1}{4} = \frac{41}{4} \quad \text{so} \quad \frac{41}{4} \times 2.5 = \frac{102.5}{4} = 25 \frac{5}{8} \text{ pounds of lasagna}
   \]

### Final Answer:
- Amanda and Sydney should order **70 pieces of chicken**.

Would you like the rest of the calculations or have any questions?

Here are 5 related questions you might explore:

1. How many pounds of deli meats should they order for the 57.5 guests?
2. How many pounds of lasagna should be ordered for the party?
3. How would the food amounts change if they only had 50 guests?
4. What if each drop-in guest counted as a full guest instead of half a guest?
5. How would the amounts change if the party was planned for 80 guests?

**Tip:** When scaling quantities in word problems, always use ratios to adjust amounts based on the number of people or items involved.

Amanda and Sydney are hosting a graduation party for 40 guests. They know there will also be guests stopping by who may have come from other parties. For ordering purposes, they will count each of these 'drop-in' guests as half a guest. How much of each food item should Amanda and Sydney order for a graduation party with 35 drop-in guests?

Learn how to calculate the correct amount of party food for 57.5 guests based on the provided proportions for 23 guests. This problem involves adjusting quantities of fried chicken, deli meats, and lasagna using ratios and multiplication. Perfect for students in Grades 6-8.

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