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what is the minimum number of cucumbers that can be planted?

To find the minimum number of cucumbers that can be planted, we need to interpret the conditions provided:

1. **Maximum number of cucumbers and tomatoes** is 300.
   - This gives us the inequality:
   \[
   C + T \leq 300
   \]
   Where \(C\) represents the number of cucumbers, and \(T\) represents the number of tomatoes.

2. **Number of tomatoes less than 100**.
   - This gives us another condition:
   \[
   T < 100
   \]

### Minimum Number of Cucumbers:
We want to minimize the number of cucumbers, which means maximizing the number of tomatoes. From the second condition, the number of tomatoes can be as large as 99 (since \(T < 100\)).

Substitute \(T = 99\) into the first inequality:
\[
C + 99 \leq 300
\]
\[
C \leq 300 - 99
\]
\[
C \leq 201
\]

Therefore, when the number of tomatoes is maximized at 99, the minimum number of cucumbers that can be planted is **201**.

Would you like further details on this? Here are some related questions you could explore:

1. What is the maximum number of cucumbers that can be planted?
2. How would the solution change if tomatoes could exceed 100?
3. What if the maximum number of cucumbers and tomatoes was 500 instead of 300?
4. How many solutions are there to the system if tomatoes are capped at 90 instead of 100?
5. How would these conditions change if cucumbers were capped at a specific value?

**Tip:** In optimization problems with multiple constraints, always check if relaxing one variable helps find the extreme value of the other.

What is the minimum number of cucumbers that can be planted?

Find the minimum number of cucumbers that can be planted based on the conditions provided: the maximum total number of cucumbers and tomatoes is 300, and the number of tomatoes must be less than 100. The solution shows how to maximize the number of tomatoes to minimize the cucumbers, resulting in a minimum of 201 cucumbers.

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