School a has 480 students and 16 classrooms school b has 192 students and 12 classroom part a what is the ratio of students to classrooms at school a part b what is the ratio of students to classrooms at school b part c how many students would have to transfer from school a to school b for the ratios of students to classroom at both schools to be the same explain your reasoning

Part A: Ratio of students to classrooms at school A:


Students: Classrooms
    480    :      16
      30    :       1        //simplify by dividing by 16 on both sides


Part B : Ratio of students to classroom at school B :


Students : Classrooms
     192    :      12
       16 .  :        1     //Simplify by dividing by 12


Part C: Number of students to transfer from School A to B:


1) Find the number of students in a classroom if both the ratios are the same.
2) Find the number of students needed to be transferred from School A to B.

Total number of students = 480 + 192 = 672
Total number of classrooms = 16 + 12 = 28
Average number of students in one class = 672 ÷ 28 = 24
If both schools have the same ratio, there should be 24 students in a class.

School B has 12 classrooms, so total number of students should be:
 12 x 24 = 288

Current number of students in School B = 192

Number of students needed to be transferred = 288 - 192 = 96

So, 96 students needed to be transferred from School A to School B so that both their students to classrooms ratios are the same.


Answers:
(a) 30 : 1
(b) 16 : 1
(c) 96 students