<think>Okay, so Alexis went shopping for job interview clothes and she had a budget of $200. She bought several items, and then she had $16 left. The question is asking how much she paid for the shoes, since she lost the receipt. Let me try to break this down step by step.

First, let's list out all the items she bought along with their prices. The known amounts are:

- Button-up shirt: $30
- Suit pants: $46
- Suit coat: $38
- Socks: $11
- Belt: $18
- Shoes: Unknown (let's call this amount "S")

She started with $200 and ended up with $16 left. So the total amount she spent should be her budget minus what's left. That would be $200 - $16 = $184. So her total expenditure is $184.

Now, the next part is adding up all her purchases to see if they total $184. If we can find the sum of all the known items and then subtract that from the total spent, we can find out how much the shoes cost.

Let's add up the known items:

Start with the shirt: $30
Add the suit pants: $30 + $46 = $76
Add the suit coat: $76 + $38 = $114
Add the socks: $114 + $11 = $125
Add the belt: $125 + $18 = $143

So, the total for the known items is $143. The shoes are the missing piece here. Since the total she spent was $184, we can set up the equation:

$143 (known items) + S (shoes) = $184 (total spent)

To solve for S:

S = $184 - $143
S = $41

Therefore, Alexis must have paid $41 for the shoes. Let me double-check the math to make sure I didn't make any errors. Adding each item again step by step: 30+46 is 76, 76+38 is 114, 114+11 is 125, 125+18 is indeed 143. Then 184 minus 143 gives 41. Looks correct. So, the shoes cost $41.
</think>

Alexis started with a budget of $200 and had $16 remaining after her purchases, so her total spending was:  
**$200 - $16 = $184**  

Next, calculate the sum of the known items:  
- Shirt: $30  
- Suit pants: $46 (**Total: $30 + $46 = $76**)  
- Suit coat: $38 (**Total: $76 + $38 = $114**)  
- Socks: $11 (**Total: $114 + $11 = $125**)  
- Belt: $18 (**Total: $125 + $18 = $143**)  

Subtract the sum of known items from the total spending to find the cost of the shoes:  
**Shoes = $184 - $143 = $41**  

**Final Answer:**  
Alexis paid \boxed{41} dollars for the shoes.