You have $100 to go shopping. A store sells shirts for $15 and dress shirts for $22. You want to spend no more then the amount of money you have. You want to leave at most $10 unspent. you need to buy at least one dress shirt. What are all the possible combinations of t shirts and dress shirts you can buy?

To find all the possible combinations of t-shirts and dress shirts that you can buy, given the conditions you mentioned, we can use a combination of algebra and logical reasoning.

Let's first establish the conditions:

1. The cost of a regular shirt is $15, and the cost of a dress shirt is $22.
2. You have $100 to spend.
3. You want to leave at most $10 unspent.
4. You need to buy at least one dress shirt.

Now, let's break down the problem step by step:

Step 1: Determine the maximum number of dress shirts you can buy.
Since you need to buy at least one dress shirt and the cost of each dress shirt is $22, the maximum number of dress shirts you can buy is given by:
Maximum dress shirts = (Total money - Unspent money) / Cost of a dress shirt

In this case:
Maximum dress shirts = ($100 - $10) / $22
Maximum dress shirts = $90 / $22 = 4 (rounded down)

Therefore, the maximum number of dress shirts you can buy is 4.

Step 2: Determine the range of t-shirts you can buy.
To find the range of t-shirts you can buy, we need to consider two possibilities:
i. You buy the maximum number of dress shirts (4) and no t-shirts.
ii. You buy the minimum number of dress shirts (1) and the rest of the money is spent on t-shirts.

i. If you buy the maximum number of dress shirts (4) and no t-shirts:
The total cost of dress shirts = 4 * $22 = $88
So, the remaining unspent money = $100 - $88 = $12

ii. If you buy the minimum number of dress shirts (1) and the rest of the money is spent on t-shirts:
The cost of a dress shirt = $22
So, the remaining money for t-shirts = $100 - $22 = $78

Considering shirts cost $15 each, the minimum and maximum number of t-shirts you can buy is given by:
Minimum t-shirts = Remaining money / Cost of a t-shirt = $12 / $15 = 0 (rounded down)
Maximum t-shirts = Remaining money / Cost of a t-shirt = $78 / $15 = 5 (rounded down)

Therefore, the range of t-shirts you can buy is from 0 to 5.

Step 3: Calculate all possible combinations.
Now that we know the maximum number of dress shirts (4) and the range of t-shirts (0 to 5), we can calculate all the possible combinations based on these values.

Here are all the possible combinations of dress shirts and t-shirts you can buy:
- 4 dress shirts, 0 t-shirts
- 3 dress shirts, 1 t-shirt
- 2 dress shirts, 2 t-shirts
- 1 dress shirt, 3 t-shirts
- 1 dress shirt, 4 t-shirts
- 1 dress shirt, 5 t-shirts

These combinations satisfy the conditions you mentioned: spending no more than $100, leaving at most $10 unspent, and buying at least one dress shirt.

Remember, these combinations are calculated based on the given conditions and may not include all possible variations within those constraints. Feel free to adjust the conditions or ask if you have any further questions!

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