Question

The school has an extra 45 cords and 30 microphones they would like to distribute these to as many classrooms as possible but with each classroom receiving the same number of power chords and the same number of microphones. ​?

Answer 1

The maximum number of classrooms that can receive the same number of cords and microphones from a supply of 45 cords and 30 microphones is determined by the greatest common divisor (GCD) of the two numbers, which is 15. The school can distribute these items to 15 classrooms, with each classroom receiving 3 cords and 2 microphones.

Step-by-step explanation:

The question involves the concept of divisibility and the greatest common divisor (GCD) since we need to find the largest number of classrooms that can each receive the same number of cords and microphones from the available supply of 45 cords and 30 microphones. We find the GCD of 45 and 30 to determine the maximum number of classrooms that can receive an equal amount of each item.

1. First, list the factors of both 45 and 30 (excluding 1 for the purpose of distribution): For 45, the factors are 3, 5, 9, 15, 45. For 30, the factors are 2, 3, 5, 6, 10, 15, 30.
2. Identify the highest common factor that both numbers share, which is 15 in this case.
3. Divide the number of cords and microphones by the GCD: 45 cords / 15 = 3 cords per classroom and 30 microphones / 15 = 2 microphones per classroom.

Therefore, the school can distribute these items to a maximum of 15 classrooms, with each classroom receiving 3 cords and 2 microphones.