Question

A theatre has 2100 seats. All of the rows of seats in the theatre have either 45 seats or 40 seats. If there are three times as many rows with 45 seats than those with 40 seats, how many rows are there?

Answer 1

The theatre with 2100 seats, having three times as many rows with 45 seats as rows with 40 seats, has a total of 48 rows.

Step-by-step explanation:

To calculate the number of rows in the theatre with 2100 seats, where there are three times as many rows with 45 seats as there are rows with 40 seats, we can set up two equations to solve the problem.

1. Let the number of rows with 40 seats be x.
2. Since there are three times as many rows with 45 seats, the number of rows with 45 seats will be 3x.
3. The total number of seats in the theatre can be represented by the equation: 40x + 45(3x) = 2100.
4. Simplify and solve for x: 40x + 135x = 2100 which simplifies to 175x = 2100.
5. Divide both sides by 175 to find x: x = 12.
6. Now calculate the total number of rows: x + 3x = 12 + 36 = 48.

Therefore, the theatre has 48 rows in total.