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Let's analyze the problem and find the correct inequality.

The situation is as follows:
- A student is ordering a flower arrangement with roses and carnations.
- She can buy any combination of these two types of flowers.
- She does not want to spend more than $30.

We define:
- $ x $: the number of roses
- $ y $: the number of carnations

The costs are:
- Each rose costs $3.
- Each carnation costs $2.

The inequality representing the total cost would account for the fact that the combined price of roses and carnations should not exceed $30.

### Setting up the inequality:
The total cost of the roses and carnations is:
\[
3x + 2y
\]

Since she does not want to spend more than $30, we write:
\[
3x + 2y \leq 30
\]

### Checking the answer options:
The correct inequality is:
\[
3x + 2y \leq 30
\]

This matches **Option B**.

### Final Answer:
The correct answer is **B**.

Would you like more details or have any questions?

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Here are some related questions to expand on this problem:
1. What if each rose cost $4 instead? How would the inequality change?
2. How would the solution change if the student wanted to spend exactly $30?
3. Can this inequality be represented graphically on a coordinate plane?
4. How would the inequality change if the student could only buy a whole number of flowers?
5. How would the inequality look if there was a minimum spend of $10?

**Tip:** When setting up inequalities in word problems, carefully identify the variables and coefficients to translate the situation correctly.

A student is ordering a flower arrangement. She can choose any combination of roses and carnations for her flower arrangement, and she does not want to spend more than $30. If roses cost $3 each and carnations cost $2 each, which inequality represents all possible combinations of x roses and y carnations?

Learn how to set up and solve an inequality to represent the cost of a flower arrangement with roses and carnations, where roses cost $3 each and carnations cost $2 each. Suitable for students in Grades 6-8.

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