Simple relationship equation major headache

[Ronb107]

Homework Statement

The quantity p varies directly with the cube of q and inversely
with the square of r. If p = 3/2, q = 1/2, and r = 1/3, which of the
following equations represents the relationship between p, q,
and r?

Homework Equations

Here's what I did...
(3/2)p = (1/2)q^3 / (1/3)r^2

The Attempt at a Solution

Could not get the answer, which is: p = (4q^3) / (3r^2)

Thanks for your help.

 

[haruspex]

(3/2)p = (1/2)q^3 / (1/3)r^2

You are quite right to write down an equation of the form p = Aq³/r², but you have not used the other information correctly. You need to find the value of A such that the given values of p, q and r are a solution to the equation.

 

[Dick]

Homework Statement

The quantity p varies directly with the cube of q and inversely
with the square of r. If p = 3/2, q = 1/2, and r = 1/3, which of the
following equations represents the relationship between p, q,
and r?

Homework Equations

Here's what I did...
(3/2)p = (1/2)q^3 / (1/3)r^2

The Attempt at a Solution

Could not get the answer, which is: p = (4q^3) / (3r^2)

Thanks for your help.

You've got the basic relation right. All that's missing is an unknown constant k. So p=kq^3/(r^2). Just put the given values in for p, q and r and solve for k.