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To solve this problem, we need to find the ratio of scoops of drink mix to gallons of water for each entry in the table. We can do this by dividing the amount of drink mix by the amount of water in each row, then confirming if the ratios are consistent.

### Step-by-Step Solution

#### Row 1:
- **Scoops of Drink Mix**: \(4 \frac{3}{4}\) = \(\frac{19}{4}\)
- **Gallons of Water**: \(1 \frac{9}{10}\) = \(\frac{19}{10}\)

To find the ratio, divide scoops by gallons:
\[
\frac{\frac{19}{4}}{\frac{19}{10}} = \frac{19}{4} \times \frac{10}{19} = \frac{10}{4} = \frac{5}{2} = 2 \frac{1}{2}
\]

#### Row 2:
- **Scoops of Drink Mix**: \(8 \frac{2}{3}\) = \(\frac{26}{3}\)
- **Gallons of Water**: \(3 \frac{7}{15}\) = \(\frac{52}{15}\)

To find the ratio, divide scoops by gallons:
\[
\frac{\frac{26}{3}}{\frac{52}{15}} = \frac{26}{3} \times \frac{15}{52} = \frac{390}{156} = \frac{5}{2} = 2 \frac{1}{2}
\]

#### Row 3:
- **Scoops of Drink Mix**: \(3 \frac{1}{2}\) = \(\frac{7}{2}\)
- **Gallons of Water**: \(1 \frac{2}{5}\) = \(\frac{7}{5}\)

To find the ratio, divide scoops by gallons:
\[
\frac{\frac{7}{2}}{\frac{7}{5}} = \frac{7}{2} \times \frac{5}{7} = \frac{35}{14} = \frac{5}{2} = 2 \frac{1}{2}
\]

### Conclusion
For each gallon of water, Sarah uses \(2 \frac{1}{2}\) scoops of drink mix.

### Answer
The answer is:
\[
2 \frac{1}{2}
\]

Would you like further clarification on any of these steps?

---

1. How do you convert mixed numbers to improper fractions?
2. What is the process of dividing fractions?
3. How do you simplify ratios?
4. Why is consistency of ratios important in this context?
5. Can this approach be used for other units?

**Tip:** When converting mixed numbers to improper fractions, multiply the whole number by the denominator, add the numerator, then place this over the original denominator.

For each gallon of water used, how many scoops of drink mix were used?

Learn how to calculate the number of scoops of drink mix per gallon of water by analyzing a table and dividing mixed numbers. This problem involves conversion to improper fractions and division of fractions, making it suitable for students in Grades 5-6.

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