Question

p varies directly as the square of q and inversely as r when p=36, q=3 and r=4 calculate q when p=200 and r=2

Answer 1

p = k (q^2)(1/r)

when p=36,q=3,r=4
so:
36 = k(9)(1/4)
k = 36(4)/9 = 16

p = 16q^2/r
when p=200, r=2
200 = 16q^2 /2
q^2 = 400/16
q = 20/4 = 5

Answer 2

p = kq^2/r, so pr/q^2 = k, a constant.

So, you want to find q such that

200*2/q^2 = 36*4/3^2
400/q^2 = 16
q^2 = 25
q = 5

Answer 3

p=k(q^2)/r
36=(k*3^2)/4
36=(9*k)/4
9*k=144
k=16

p=16(q^2)/r
200=(16*q^2)/2
16*q^2=400
q^2=400/16
q^2=25
q=√25
q=5