Discussion
Girls
For every two Teacher there are 30 girls.
That means that every teacher has 30/2 = 15 girls.
Boys
For every three teachers there are 60 boys
So every teacher must teach 60/3 = 20 boys.
Both
The teacher load for every teacher is 20 + 15 = 35 students.
Proportion
1/35 = T/(432 - T) Remember you have to take out the number of Teachers from the total number of people in the building. Cross multiply.
432 - T = 35T Add T to Both sides.
432 = 35T + T
432 = 36T Divide by 36
T = 432 / 36
T = 12 So there are 12 Teachers in the Building
Girls in the Building
Every teacher teaches 15 girls
1 teacher /12 teachers = 15 girls/x Cross multiply
x = 12 * 15
x = 180 girls are in that school.
Boys in the Building
1 teacher teaches 20 boys
12 teachers teach x
1/12 = 20 / x Cross multiply
12*20 = x
240 = x
There are 240 boys in the building.
Summary For the School
Teachers = 12
Boys = 240
Girls = 180
Nice problem. Thanks for posting.