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Let's solve the problem step-by-step using the information given:

The ratio of students wearing sneakers to those wearing boots is \( 5:6 \). This means that for every 5 students wearing sneakers, there are 6 students wearing boots.

### Step 1: Understanding the Total Ratio Parts
The total number of parts in the ratio is:
\[
5 + 6 = 11 \text{ parts}
\]

### Step 2: Finding the Value of One Part
Given that there are 33 students in total, we divide this number by the total parts of the ratio:
\[
\text{One part} = \frac{33}{11} = 3
\]

### Step 3: Calculating the Number of Students Wearing Sneakers
Since the ratio for sneakers is 5 parts:
\[
\text{Students wearing sneakers} = 5 \times 3 = 15
\]

### Step 4: Calculating the Number of Students Wearing Boots
For boots, which is 6 parts:
\[
\text{Students wearing boots} = 6 \times 3 = 18
\]

### Step 5: Verifying the Total
Adding the number of students wearing sneakers and boots together:
\[
15 + 18 = 33
\]
This matches the total number of students, confirming that our solution is correct.

### Answer
- **15 students are wearing sneakers.**

Would you like more details or have any questions about this solution?

Here are some related questions for further practice:
1. If the ratio of students wearing sneakers to boots changes to 7:8, how many would be wearing sneakers if there are 45 students in total?
2. What if 24 students were wearing boots and the ratio remained the same; how many would be wearing sneakers?
3. How would the number of students change if the ratio became 2:3 but the total students were still 33?
4. If there were 50 students and the same ratio, how many students would wear each type of footwear?
5. Can you express the ratio of students wearing sneakers to the total number of students?

**Tip:** When working with ratios, always check that the sum of the parts matches the total given to verify your calculations.

The ratio of students wearing sneakers to those wearing boots is 5 to 6. If there are 33 students in the class, and all of them are wearing either sneakers or boots, how many of them are wearing sneakers?

Solve the problem of finding the number of students wearing sneakers given a ratio of 5:6 and a total of 33 students. This example demonstrates using ratios and proportions to solve real-world math problems, suitable for students in Grades 6-8.

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