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We are tasked with finding the unit rate in grams of drink mix per ounce of water. The problem involves dividing two mixed numbers:

- \( 19 \frac{1}{4} \) grams of drink mix 
- \( 1 \frac{3}{4} \) ounces of water

### Step 1: Convert mixed numbers to improper fractions.

1. \( 19 \frac{1}{4} = \frac{77}{4} \) (since \( 19 \times 4 + 1 = 77 \)).
2. \( 1 \frac{3}{4} = \frac{7}{4} \) (since \( 1 \times 4 + 3 = 7 \)).

### Step 2: Calculate the unit rate by dividing \( \frac{77}{4} \) grams by \( \frac{7}{4} \) ounces.

Dividing fractions is equivalent to multiplying by the reciprocal:

\[
\frac{77}{4} \div \frac{7}{4} = \frac{77}{4} \times \frac{4}{7} = \frac{77 \times 4}{4 \times 7} = \frac{308}{28} = 11
\]

So, the unit rate is **11 grams per ounce of water**.

### Answer:
The correct answer is **11**.

Would you like further details or have any additional questions?

Here are 5 questions to extend this problem:
1. How do you convert improper fractions back into mixed numbers?
2. What happens if the number of ounces of water changes?
3. How would the unit rate change if Cindy dissolved less mix?
4. Can you think of other real-life situations where unit rate calculations are useful?
5. How do you simplify more complex fractions in unit rate problems?

**Tip**: Always double-check whether you're dividing or multiplying when dealing with fractions to avoid mistakes.

Cindy dissolves 19 1/4 grams of drink mix in 1 3/4 ounces of water. What is the unit rate in grams of drink mix per ounce of water?

Learn how to calculate the unit rate of drink mix per ounce of water. This problem involves dividing mixed numbers and simplifying fractions. Suitable for students in Grades 6-8.

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