A plane has 
360 total seats, which are divided into economy class and business class. For every 
13 seats in economy class, there are 
5 seats in business class.
How many seats are there in each class?

Let the number of seats in economy class be \( x \) and the number of seats in business class be \( y \). We are given the following information:

1. The total number of seats is 360:
   \[
   x + y = 360
   \]
   
2. The ratio of economy class seats to business class seats is 13:5, meaning:
   \[
   \frac{x}{y} = \frac{13}{5}
   \]

We can solve this system of equations step-by-step.

### Step 1: Express \( x \) in terms of \( y \) using the ratio:
\[
\frac{x}{y} = \frac{13}{5} \quad \Rightarrow \quad x = \frac{13}{5}y
\]

### Step 2: Substitute this expression for \( x \) into the total number of seats equation:
\[
\frac{13}{5}y + y = 360
\]

### Step 3: Combine like terms:
\[
\frac{13}{5}y + \frac{5}{5}y = 360 \quad \Rightarrow \quad \frac{18}{5}y = 360
\]

### Step 4: Solve for \( y \):
\[
y = 360 \times \frac{5}{18} = 100
\]

So, there are 100 business class seats.

### Step 5: Use the total number of seats equation to find \( x \):
\[
x + 100 = 360 \quad \Rightarrow \quad x = 360 - 100 = 260
\]

Thus, there are 260 economy class seats and 100 business class seats.

### Final Answer:
- Economy class seats: 260
- Business class seats: 100

Would you like further details or have any questions?

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Here are some related questions:
1. What if the total number of seats was 400? How would that change the number in each class?
2. How can the seat distribution change if the ratio were 2:1 instead of 13:5?
3. If there were an additional 50 seats added to the economy class, how many total seats would there be?
4. How does changing the ratio to 10:3 affect the distribution of seats?
5. What happens to the seat counts if 10 business seats are removed?

**Tip**: When working with ratios, always try to express one variable in terms of the other to simplify calculations.

A plane has 360 total seats, which are divided into economy class and business class. For every 13 seats in economy class, there are 5 seats in business class. How many seats are there in each class?

Find out how to solve the problem of distributing 360 seats on a plane between economy and business class using a 13:5 ratio. This step-by-step guide uses algebra and ratio equations to determine the number of seats in each class. Suitable for students in Grades 8-10.

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