high school # of band memebers

logan 75
Northeast 90

during the halftime show, the bands plan to march into the stadium from opposite ends using formations with the same # of rows. If the bands match up in the center of the field what is the maximum number os rows, and how many members will be in each row??

Well, it sounds like Logan and Northeast High School are going to have quite the symphonic showdown! To determine the maximum number of rows and how many members will be in each row, let's do some clown calculations, shall we?

If Logan High School has 75 band members and Northeast High School has 90 band members, we need to find a common number of rows that is a factor of both 75 and 90. This way, each row can have the same number of members.

The factors of 75 are 1, 3, 5, 15, 25, and 75. The factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, and 90.

Looking for a common factor, we see that 15 is the largest number that both 75 and 90 share. Therefore, the maximum number of rows they can have is 15.

Now, if we divide the number of band members from each school by the common number of rows (15), we can find out how many members will be in each row.

For Logan High School: 75 band members / 15 rows = 5 members per row.
For Northeast High School: 90 band members / 15 rows = 6 members per row.

So, in conclusion, when the bands meet at the center of the field, they can have a maximum of 15 rows. Each row from Logan High School will have 5 band members, and each row from Northeast High School will have 6 band members.

It's going to be quite the symphonic spectacle, with dueling rows of musicians!

To determine the maximum number of rows and the number of members in each row, we can use the concept of finding the greatest common divisor (GCD) of the number of band members for Logan High School and Northeast High School.

Given that Logan High School has 75 band members and Northeast High School has 90 band members, we need to find the GCD of these two numbers.

The prime factors of 75 are: 3 * 5 * 5
The prime factors of 90 are: 2 * 3 * 3 * 5

To find the GCD, we take the common factors in the prime factorization of both numbers: 3 * 5 = 15.

Therefore, the maximum number of rows that the bands can form with the same number of members in each row is 15, and there will be 75/15 = 5 members in each row for Logan High School and 90/15 = 6 members in each row for Northeast High School.

To find the maximum number of rows and the number of members in each row, you need to determine the common factors of the number of band members from Logan High School (75) and Northeast High School (90).

Here's how you can do it:

Step 1: Find all the factors of 75:
The factors of 75 are: 1, 3, 5, 15, 25, and 75.

Step 2: Find all the factors of 90:
The factors of 90 are: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, and 90.

Step 3: Identify the common factors:
The common factors of 75 and 90 are: 1, 3, 5, and 15.

Step 4: Choose the largest common factor:
The largest common factor is 15.

Therefore, the maximum number of rows the bands can form is 15, and each row will have 15 members from each band.

Please note that this solution assumes an equal number of members in each row from both bands.