Brandon is shopping at Old Navy during a sale. All shorts are $16 each and all t-shirts are $10 each. He has $100 to spend and would like to purchase at least 2 pairs of shorts.

Let's break down Brandon's shopping scenario:

- **Price of each pair of shorts**: $16
- **Price of each t-shirt**: $10
- **Total money Brandon has**: $100
- **Minimum pairs of shorts Brandon wants to buy**: 2 pairs

### Variables:
Let:
- $ s $ represent the number of pairs of shorts.
- $ t $ represent the number of t-shirts.

### Constraints:
1. **Total cost**: The total cost for shorts and t-shirts must be less than or equal to $100.
   \[
   16s + 10t \leq 100
   \]
2. **At least 2 pairs of shorts**: Brandon wants to buy at least 2 pairs of shorts.
   \[
   s \geq 2
   \]

### Steps to Determine Possible Purchases:
1. **Substitute $ s = 2 $ (minimum number of shorts) into the total cost equation**:
   \[
   16(2) + 10t \leq 100
   \]
   \[
   32 + 10t \leq 100
   \]
   \[
   10t \leq 68
   \]
   \[
   t \leq 6.8
   \]
   Since $ t $ must be an integer, $ t $ can be at most 6.

   Therefore, if Brandon buys 2 pairs of shorts, he can buy up to 6 t-shirts.

2. **Other scenarios**:
   - **If Brandon buys 3 pairs of shorts**:
     \[
     16(3) + 10t \leq 100
     \]
     \[
     48 + 10t \leq 100
     \]
     \[
     10t \leq 52
     \]
     \[
     t \leq 5.2
     \]
     So $ t $ can be at most 5.

   - **If Brandon buys 4 pairs of shorts**:
     \[
     16(4) + 10t \leq 100
     \]
     \[
     64 + 10t \leq 100
     \]
     \[
     10t \leq 36
     \]
     \[
     t \leq 3.6
     \]
     So $ t $ can be at most 3.

### Conclusion:
Brandon has several options depending on how many pairs of shorts he buys. For example:
- 2 pairs of shorts and up to 6 t-shirts.
- 3 pairs of shorts and up to 5 t-shirts.
- 4 pairs of shorts and up to 3 t-shirts.

### Questions to Consider:
1. What is the maximum number of t-shirts Brandon can buy if he purchases only 2 pairs of shorts?
2. If Brandon decides to buy 5 t-shirts, how many pairs of shorts can he afford?
3. How many different combinations of shorts and t-shirts can Brandon purchase with $100?
4. If the price of shorts increases to $18 each, how does that affect the number of t-shirts he can buy?
5. What happens if Brandon wants to buy at least 3 pairs of shorts instead?

### Tip:
**Prioritize Budgeting**: Always calculate the cost of essentials (shorts, in this case) first, then see what remains for additional items (t-shirts). This approach helps in managing money effectively while still getting what you need.

Explore Brandon's shopping dilemma at Old Navy during a sale. Calculate how many pairs of shorts and t-shirts he can buy with $100. Discover the optimal combinations of shorts and t-shirts while meeting his budget. Suitable for Grades 7-9.

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