45% of the students in a class are girls and the number of boys exceeds the number of girls by 30. How many students are there in the class?


Let's solve this problem step by step.

### Step 1: Define the variables
Let the total number of students in the class be \( x \). 

### Step 2: Express the number of girls
According to the problem, 45% of the students are girls. So, the number of girls can be expressed as:
\[
\text{Number of girls} = 0.45x
\]

### Step 3: Express the number of boys
The number of boys exceeds the number of girls by 30, so:
\[
\text{Number of boys} = \text{Number of girls} + 30 = 0.45x + 30
\]

### Step 4: Set up the equation
Since the total number of students is the sum of the number of boys and girls, we have:
\[
x = \text{Number of girls} + \text{Number of boys}
\]
Substitute the expressions from above:
\[
x = 0.45x + (0.45x + 30)
\]

### Step 5: Solve the equation
Simplify the equation:
\[
x = 0.45x + 0.45x + 30
\]
\[
x = 0.9x + 30
\]
Now, subtract \( 0.9x \) from both sides:
\[
x - 0.9x = 30
\]
\[
0.1x = 30
\]
Divide both sides by 0.1:
\[
x = \frac{30}{0.1} = 300
\]

### Step 6: Conclusion
The total number of students in the class is \( 300 \).

Would you like more details or have any questions?

Here are five related questions:
1. How would the problem change if the percentage of girls was 55% instead?
2. What if the number of boys exceeded the number of girls by a different number, like 50?
3. How do you determine the number of boys once the total number of students is known?
4. What if the problem only gave the number of boys and not the percentage of girls?
5. How can you check if your solution is correct?

**Tip:** Always double-check your final answer by plugging it back into the original problem to see if it makes sense.

Learn how to solve a math problem involving percentages and equations. This problem calculates the total number of students in a class where 45% are girls and boys exceed girls by 30. Suitable for Grades 6-8.

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