There are 450 students in the school of academic studies. The ratio of female students to male students is 5:4, how many male and female students are there in the school?

To solve this problem, we can use the given ratio of female to male students, which is 5:4. Let's break this down step by step.

### Step 1: Set Up the Ratio
Let the number of female students be \( 5x \) and the number of male students be \( 4x \), where \( x \) is a common multiplier.

### Step 2: Use the Total Number of Students
We know the total number of students is 450. Therefore, we can write the equation:

\[
5x + 4x = 450
\]

### Step 3: Simplify the Equation
Combine the terms on the left-hand side:

\[
9x = 450
\]

### Step 4: Solve for \( x \)
Divide both sides by 9 to find \( x \):

\[
x = \frac{450}{9} = 50
\]

### Step 5: Find the Number of Female and Male Students
Now that we know \( x = 50 \):
- The number of female students is \( 5x = 5 \times 50 = 250 \).
- The number of male students is \( 4x = 4 \times 50 = 200 \).

### Final Answer:
- **Number of female students**: 250
- **Number of male students**: 200

Would you like more details, or do you have any questions?

Here are some related questions to consider:
1. What would the ratio be if there were 300 female students?
2. If the ratio changed to 3:2, how many male students would there be?
3. How many students would there be if the ratio remained 5:4 but there were 300 male students?
4. If 10 male students transferred out, what would the new ratio of females to males be?
5. How would the total number of students change if both the female and male student numbers doubled?

**Tip:** When working with ratios, always remember to check if the total matches the sum of the parts before finalizing your answer.

Discover how to solve a ratio problem involving 450 students where the ratio of female to male students is 5:4. This solution includes a step-by-step breakdown using basic algebraic concepts, suitable for students in Grades 5-7.

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