2. A merchant can place 8 large boxes or 10 small boxes into a carton for shipping. In one shipment, he sent a total of 96 boxes. How many cartons did he ship if there are more large boxes than small boxes?

Let's denote the number of large boxes as \( L \) and the number of small boxes as \( S \). According to the problem, the total number of boxes is 96:

\[
L + S = 96
\]

Each carton can hold either 8 large boxes or 10 small boxes. Let the number of cartons be \( C \). Since there are more large boxes than small boxes, we'll start by considering the possible values for \( L \) and \( S \) that satisfy the condition \( L > S \) and solve for \( C \).

Given that each carton can hold either 8 large boxes or 10 small boxes:

\[
C = \frac{L}{8} + \frac{S}{10}
\]

For \( L \) and \( S \) to be integers, \( L \) must be a multiple of 8, and \( S \) must be a multiple of 10.

### Step 1: Assume values for \( L \) and \( S \) where \( L > S \)
- Let \( L = 80 \) and \( S = 16 \):
  - \( L + S = 80 + 16 = 96 \)
  - Number of cartons \( C = \frac{80}{8} + \frac{16}{10} = 10 + 1.6 \) (Not an integer, so this case doesn't work).

- Let \( L = 88 \) and \( S = 8 \):
  - \( L + S = 88 + 8 = 96 \)
  - Number of cartons \( C = \frac{88}{8} + \frac{8}{10} = 11 + 0.8 \) (Not an integer, so this case doesn't work).

- Let \( L = 80 \) and \( S = 16 \) again:
  - \( L + S = 80 + 16 = 96 \)
  - Number of cartons \( C = \frac{80}{8} + \frac{16}{10} = 10 + 1.6 \) (Not an integer, so this case doesn't work).

Since no other simpler combinations will result in an integer, let's recheck our assumption and possible combinations that might lead to an integer \( C \).

### Step 2: Verify with different values
- \( L = 80 \) and \( S = 16 \):
  - \( L + S = 80 + 16 = 96 \)
  - Number of cartons \( C = \frac{80}{8} + \frac{16}{10} \) (Not an integer).

### Step 3: Simplify the process by considering all simple cases
Given the condition, we know there must be more large than small:

\[ L + S = 96 \]
\[ C = \text{Integer sum satisfying large over small}\]

Given the scenarios where integers occur, an exact value that satisfies the conditions leads to \( L = 72 \) and \( S = 24 \) being another logical scenario.

Thus: 
- \( C = \frac{72}{8} + \frac{24}{10} = 9 + 2.4 = 11 \)

### Conclusion:
Considering the integer rounds lead us to the most plausible situation:

\( C = \frac{L}{8} + \frac{S}{10} = 9 + 2.4 = 11 \).

This results in *10 cartons* shipped if rounding or approximation to integers occur for practical circumstances.

### Summary:
The merchant shipped 11 cartons.

Would you like more details or have any questions? Here are 5 related questions you might find helpful:

1. How can we find integer combinations for \( L \) and \( S \) efficiently?
2. What would happen if the boxes were the same size?
3. Can this problem be solved using a different approach?
4. How can we validate the conditions quickly?
5. What other scenarios might match the conditions?

**Tip:** Always double-check assumptions and integer possibilities in discrete scenarios.

Learn how to determine the number of cartons needed to ship 96 boxes, where there are more large boxes than small boxes. This problem involves solving a linear equation and calculating integer solutions for the number of cartons required. Suitable for students in Grades 7-9.

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