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The problem in the image states:

"Fabian harvests 10 pounds of tomatoes from his garden. He needs \( 2 \frac{2}{5} \) pounds to make a batch of soup. If he sets aside 2.8 pounds of tomatoes to make spaghetti sauce, how many batches of soup can Fabian make? Write and solve an equation."

### Step-by-step solution:

1. **Convert the mixed number \( 2 \frac{2}{5} \) to an improper fraction**:
   \[
   2 \frac{2}{5} = \frac{12}{5}
   \]
   So, Fabian needs \( \frac{12}{5} \) pounds of tomatoes per batch of soup.

2. **Subtract the tomatoes set aside for spaghetti sauce**:
   Fabian has 10 pounds of tomatoes, but he sets aside 2.8 pounds for spaghetti sauce, so the remaining tomatoes for soup are:
   \[
   10 - 2.8 = 7.2 \text{ pounds}
   \]

3. **Set up the equation**:
   Let \( x \) represent the number of batches of soup he can make. Each batch requires \( \frac{12}{5} \) pounds of tomatoes. The total amount of tomatoes used for \( x \) batches is \( x \times \frac{12}{5} \). This total should equal the 7.2 pounds of tomatoes he has left:
   \[
   x \times \frac{12}{5} = 7.2
   \]

4. **Solve the equation**:
   To solve for \( x \), multiply both sides by \( \frac{5}{12} \):
   \[
   x = 7.2 \times \frac{5}{12}
   \]
   First, simplify the multiplication:
   \[
   7.2 \times \frac{5}{12} = \frac{7.2 \times 5}{12} = \frac{36}{12} = 3
   \]

Thus, Fabian can make **3 batches of soup**.

### Summary:
- **Tomatoes left after setting aside for spaghetti sauce**: 7.2 pounds.
- **Tomatoes required per batch of soup**: \( \frac{12}{5} \) pounds.
- **Number of batches Fabian can make**: 3.

Let me know if you'd like further details on any of these steps!

### Follow-up questions:
1. How would the solution change if Fabian needed more tomatoes per batch?
2. What if Fabian harvested fewer tomatoes, say 8 pounds? How many batches could he make then?
3. If Fabian sets aside different amounts for spaghetti sauce, how would you adjust the equation?
4. Can you convert other mixed fractions like \( 3 \frac{1}{4} \) into improper fractions for practice?
5. How would you solve this if Fabian needed \( \frac{5}{6} \) pounds of tomatoes per batch instead?

### Tip:
Always convert mixed numbers to improper fractions for easier calculations in word problems!

Fabian harvests 10 pounds of tomatoes from his garden. He needs 2 2/5 pounds to make a batch of soup. If he sets aside 2.8 pounds of tomatoes to make spaghetti sauce, how many batches of soup can Fabian make? Write and solve an equation.

Fabian harvests 10 pounds of tomatoes and needs 2 2/5 pounds per batch of soup. After setting aside 2.8 pounds for spaghetti sauce, find how many batches of soup he can make. Learn the step-by-step solution using fractions and algebra.

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