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### Problem Summary:
- **Initial purchase**: 21 ½ gallons of lemonade.
- **Additional purchase by the teacher**: 5 ¼ gallons of lemonade.
- **Leftover lemonade at the end of the day**: 1 ¾ gallons of lemonade.
- **Question**: How much lemonade was consumed during the day?

### Step-by-Step Solution:
1. **Convert mixed numbers to improper fractions**:
   - \( 21 \frac{1}{2} \) = \( \frac{43}{2} \) gallons.
   - \( 5 \frac{1}{4} \) = \( \frac{21}{4} \) gallons.
   - \( 1 \frac{3}{4} \) = \( \frac{7}{4} \) gallons.

2. **Total lemonade available**:
   - Add the initial purchase and the teacher’s additional purchase:
   \[
   \frac{43}{2} + \frac{21}{4}
   \]
   First, find a common denominator (4):
   \[
   \frac{43}{2} = \frac{86}{4}
   \]
   Now add:
   \[
   \frac{86}{4} + \frac{21}{4} = \frac{107}{4}
   \]
   Total lemonade available = \( \frac{107}{4} \) gallons.

3. **Lemonade consumed**:
   The school has 1 ¾ gallons left at the end of the day, or \( \frac{7}{4} \) gallons. To find out how much lemonade was consumed, subtract the leftover from the total lemonade available:
   \[
   \frac{107}{4} - \frac{7}{4} = \frac{100}{4} = 25 \text{ gallons}.
   \]

### Answer:
The amount of lemonade consumed during the day is **25 gallons**.

Would you like further details or have any questions about the process?

Here are 5 related questions you can explore:
1. How do you convert between mixed numbers and improper fractions?
2. How do you find a common denominator when adding fractions?
3. How can you verify your subtraction of fractions in this problem?
4. What is the significance of improper fractions in real-world problems?
5. How would the solution change if there was no leftover lemonade?

**Tip**: Always ensure that your fractions have the same denominator when adding or subtracting them to avoid errors.

For school spirit day, the school purchases 21 1/2 gallons of lemonade. During the day, a teacher buys an additional 5 1/4 gallons of lemonade. At the end of the day, the school has 1 3/4 gallons of lemonade left. How much lemonade is consumed during the day?

Solve a problem involving the consumption of lemonade using mixed numbers and fractions. The school purchases 21 1/2 gallons of lemonade, a teacher adds 5 1/4 gallons, and 1 3/4 gallons are left at the end of the day. Learn how to find the total lemonade consumed.

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