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 find the number of male and female students in the school, we can use the given ratio of female to male students, which is 5:4. Let's denote:

- The number of female students as \( F \)
- The number of male students as \( M \)

Given the ratio \( F : M = 5 : 4 \), we can write:

\[
\frac{F}{M} = \frac{5}{4}
\]

This implies that:

\[
F = 5x \quad \text{and} \quad M = 4x
\]

where \( x \) is a common multiplier.

The total number of students is given as 450:

\[
F + M = 450
\]

Substitute the expressions for \( F \) and \( M \):

\[
5x + 4x = 450
\]

Simplify the equation:

\[
9x = 450
\]

Solve for \( x \):

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

Now, substitute \( x = 50 \) back to find \( F \) and \( M \):

\[
F = 5x = 5 \times 50 = 250
\]

\[
M = 4x = 4 \times 50 = 200
\]

So, there are **250 female students** and **200 male students** in the school.

### Summary:
- Female students: 250
- Male students: 200

Would you like more details or have any other questions?

### Relative Questions:
1. What would be the number of male and female students if the ratio was 3:2 instead?
2. How would the numbers change if there were 500 students in total, keeping the ratio 5:4?
3. What is the percentage of female students in the school?
4. If 10 male students leave the school, what would the new ratio of female to male students be?
5. How would you express the ratio of male to female students?

**Tip:** Remember that ratios can always be scaled up or down by multiplying or dividing by the same number to maintain the same relationship between quantities.

Solve the problem of finding the number of male and female students in a school with a total of 450 students and a given ratio of 5:4. This solution covers the application of ratios and basic algebra to find the exact numbers, suitable for Grades 6-8.

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