In a school, there are three houses : Red, Blue , and Green. Each houses has a certain number of students, and each student must choose to travel to either the Museum or Red Fort. The total number of students accross all three houses is 800, with the Red House having 350 students. Students travelling to the Museum : The Blue house has 150 students.the total number of males and total number of females from the Red and Green houses together are equal.The Red House has an equal number of males and females. Students Travelling to the Red Fort : the Green house has 120 Students, which is twice the number of students in the Blue house. The number of students from the Red House is 60% of the total number of students from all houses travelling to the Red Fort . The ratio of males to females in the Red, Blue, and Green houses is 3:2, 1:1, and 5:1 , respectively.

Let's analyze the information given and break it down step by step.

### Step 1: Total Students and House Distribution
- **Total number of students:** 800
- **Red House students:** 350
- **Blue House students:** Let this be \( B \)
- **Green House students:** Let this be \( G \)

Therefore, \( 350 + B + G = 800 \), which simplifies to:
\[
B + G = 450
\]

### Step 2: Distribution of Students Traveling to Museum and Red Fort
#### Students Traveling to the Museum:
- **Blue House students:** 150
- **Total number of males and females from the Red and Green houses traveling to the Museum are equal.**
- **Red House has an equal number of males and females.**

#### Students Traveling to the Red Fort:
- **Green House students:** 120, which is twice the number of students from the Blue House traveling to the Red Fort.
  
Let \( x \) be the number of Blue House students traveling to the Red Fort. Then:
\[
2x = 120 \implies x = 60
\]

- **Number of students from the Red House traveling to the Red Fort is 60% of the total number of students from all houses traveling to the Red Fort.**

Let \( y \) be the number of Red House students traveling to the Red Fort, and let \( z \) be the total number of students traveling to the Red Fort. Then:
\[
y = 0.6z
\]
\[
z = y + 60 + 120
\]

### Step 3: Ratios of Males to Females in Each House
- **Red House:** Ratio of males to females is 3:2.
- **Blue House:** Ratio of males to females is 1:1.
- **Green House:** Ratio of males to females is 5:1.

### Step 4: Solve the System of Equations

#### Travel to Red Fort:
\[
z = 0.6z + 60 + 120
\]
Solving for \( z \):
\[
z - 0.6z = 180 \implies 0.4z = 180 \implies z = \frac{180}{0.4} = 450
\]
Thus, \( y = 0.6 \times 450 = 270 \).

#### Travel to Museum:
\[
\text{Total students traveling to Museum} = 800 - 450 = 350
\]
- Blue House students traveling to Museum = 150
- Green House students traveling to Museum = \( G - 120 \)
- Red House students traveling to Museum = \( 350 - 270 = 80 \)

Given the above, the number of students in the Green House is \( G \), and \( G = 270 - 150 \).

Now we solve:

1. \( G + B = 450 \)
2. \( G = 60 + 120 + 60 \)

Finally, use the ratios to determine the number of males and females in each house.

Let me know if you'd like the full expansion and further solution or have any other questions!

Explore a detailed analysis of school house distribution and student travel patterns involving the Red, Blue, and Green houses. Understand how to solve equations and analyze ratios based on the given student data. Suitable for students in Grades 7-9.

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