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.