the number of boys varied inversely as the number of teachers and directly as the number or girls squared

Question

When there were 200 boys, there were 10 girls and 20 teachers. How many boys were there when there were 2 teachers and 8 girl?

 

Please help me understand how to created the equation when they vary inversely or directly.

Answer 1

if x varies directly with y then
when y increases, so does x.. and when
y decreases, so does x
The basic equation is: x = ky

If x varies inversely with y then x = k/y
When y gets larger, x gets smaller and
vuce versa.
K is the constant of proportion which we have to find.

Let b= boys, g=girls, t=teachers

b = k/t for inverse proportion to teachers
b= kg² for direct proportion to # girls squared

Our equation looks like:

 

b= (kg²)/t

 

From given information we find the value of k

 

200 = k(10²)/20

200 = 100k/20

200 = 5k

k = 40

 

using k = 40 and b=kg²/t we get

 

b = 40(8²)/2

b= 20(64)

b= 1280

 

there were 1280 boys when there are

8 girls and 2 teachers.  Hope this helps.