Question

For every 2 teachers there are 30 girl students. For every 3 teachers there are 60 boy students. If there are 432 people in the school how many boys,girls and teachers

Answer 1

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.