School A has 480 students and 16 classrooms, School B has 192 students and 12 classrooms.

How many students would have to transfer from School A to School B for the ratios of students to classrooms at both schools to be the same? Explain your answer.

Steve already answered this.

http://www.jiskha.com/display.cgi?id=1429320500

Is there a shorter way to solve this problem than the equation that was given.

You're kidding??!!

A shorter way than this??

"If x students transfer,

(480-x)/16 = (192+x)/12
x = 96

I don't think so.

No

To determine the number of students that would need to transfer from School A to School B for the ratios of students to classrooms to be the same, we need to understand and compare the ratios of students to classrooms at both schools.

The ratio of students to classrooms can be found by dividing the total number of students by the total number of classrooms. Let's calculate these ratios for both schools:

For School A:
Number of students: 480
Number of classrooms: 16
Ratio of students to classrooms = (Number of students) / (Number of classrooms) = 480 / 16 = 30

For School B:
Number of students: 192
Number of classrooms: 12
Ratio of students to classrooms = (Number of students) / (Number of classrooms) = 192 / 12 = 16

Currently, the ratio for School A is 30 students per classroom, while the ratio for School B is 16 students per classroom.

To find the number of students that would need to transfer from School A to School B for the ratios to be the same, we need to set up an equation.

Let's say "x" represents the number of students that would transfer from School A to School B.

After the transfers, the number of students in School A would be 480 - x, and the number of students in School B would be 192 + x.

Now, let's set up the equation using the ratios:

(480 - x) / 16 = (192 + x) / 12

To solve for "x", we can cross-multiply and then solve the resulting equation:

12 * (480 - x) = 16 * (192 + x)

5760 - 12x = 3072 + 16x

Combine like terms:

28x = 2688

Divide both sides by 28:

x = 96

Therefore, 96 students would need to transfer from School A to School B for the ratios of students to classrooms at both schools to be the same.

It's important to note that transferring students not only affects the ratio of students to classrooms but also other factors such as overall class size, teacher-student ratios, and available resources. These aspects should be considered when making decisions regarding student transfers.