Find proportions when there are 2 variables

[P-Illiterate]

a is proportional to square root of (b *t²)
a is proportional to 1/c³

a is 5, when b = 9, t = 2, c = 3

Find a' when b'=25, t'=2, c'=5

My attempt:

= (25 root 5/12 root 3) 5

I think my steps are wrong, can someone help me!?

 

[CompuChip]

I think you are getting confused by the a / a' notation.

a is proportional to square root of (b *t²)
a is proportional to 1/c³

Let's start with this part. This means, that a contains both those factors, so you can write it as
$$a(b, t, c) = \frac{\sqrt{b t^2}}{c^3} \cdot k$$
The k here is some constant number (the proportionality factor). Note that I have written the left hand side as if it were a function of b, t and c.

Now, you know that a(b = 9, t = 2, c = 3) equals 5, you can use that to calculate the proportionality constant k.

 

[P-Illiterate]

Thank you so much for the help :)