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Let's go through each problem and solve them step-by-step.

### Problem 13
Mr. Holland goes to Mudd Hut and gets 6 cups of coffee for $19.50. We need to find:
1. The cost of one cup of coffee.
2. The cost of 15 cups of coffee.

#### Solution:
1. **Cost of one cup of coffee**:
   - Total cost for 6 cups = $19.50
   - Cost per cup = $ \frac{19.50}{6} \approx 3.25 $ dollars per cup.

2. **Cost of 15 cups**:
   - Cost of 15 cups = $ 15 \times 3.25 = 48.75 $ dollars.

So, the answers are:
- **a. $3.25**
- **b. $48.75**

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### Problem 14
Jeremy can row $ \frac{2}{3} $ of a mile in $ \frac{2}{9} $ of an hour. We need to find his unit rate in miles per hour.

#### Solution:
1. To find miles per hour, we divide the distance by the time:
   - $ \text{Unit rate} = \frac{\frac{2}{3} \text{ miles}}{\frac{2}{9} \text{ hours}} $.
2. Dividing by a fraction is the same as multiplying by its reciprocal:
   - $ \frac{2}{3} \div \frac{2}{9} = \frac{2}{3} \times \frac{9}{2} = 3 $ miles per hour.

So, **Jeremy’s unit rate is 3 miles per hour**.

---

### Problem 15
A lizard's tail grows back at a constant rate after 6 weeks, reaching $ 3 \frac{3}{4} $ inches. We need to find the growth rate per week.

#### Solution:
1. Convert $ 3 \frac{3}{4} $ to an improper fraction: $ 3 \frac{3}{4} = \frac{15}{4} $.
2. Divide the total length by 6 weeks:
   - Growth per week = $ \frac{\frac{15}{4}}{6} = \frac{15}{4} \times \frac{1}{6} = \frac{15}{24} = \frac{5}{8} $ inches per week.

So, **the lizard’s tail grows $ \frac{5}{8} $ inches each week**.

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### Problem 16
Antonio is making tomato basil soup, and the recipe uses the following ingredients. If he needs to make more than the recipe amount, calculate the quantity needed for each ingredient if he uses 1 cup of milk.

#### Solution:
- **Given quantities in the table:**
  - Tomatoes: $ \frac{1}{3} $ cup
  - Milk: 1 cup
  - Basil: $ \frac{1}{4} $ cup
  - Chicken Broth: $ \frac{1}{2} $ cup

Since he uses **1 cup of milk** (which matches the table), the quantities for other ingredients remain the same:
- **Tomatoes**: $ \frac{1}{3} $ cup
- **Basil**: $ \frac{1}{4} $ cup
- **Chicken Broth**: $ \frac{1}{2} $ cup

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Would you like more detailed explanations for any of these problems?

### Related Questions to Explore:
1. How do you determine proportional relationships in a word problem?
2. How can unit rates involving fractions be simplified further?
3. Why is it useful to convert mixed numbers to improper fractions in calculations?
4. What are real-life applications of unit rates in activities like rowing?
5. How do we adjust ingredient proportions when changing recipe quantities?

**Tip**: When dealing with unit rates or proportions, always double-check whether you're using the correct units for each measurement.

Solve problems involving proportional relationships, unit rates, and fractional calculations from the given worksheet.

Step-by-step solutions for a 7th-grade worksheet covering proportional relationships, unit rates, and fractional calculations. Learn to calculate cost per cup, miles per hour, weekly growth rates, and ingredient adjustments in recipes.

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