It is known that the quantities p and q are inversely proportional and the quantities q and r are inversely

It is known that the quantities p and q are inversely proportional and the quantities q and r are inversely proportional. What can be said about the values of p and r: a) they are directly proportional; b) they are inversely proportional; c) they can be neither directly proportional nor inversely proportional?

Let us denote the proportionality of the given values using the formula: p = a / q, q = b / r. (1) Since the question is about the ratio of p and r, then most likely they are directly proportional, but you need to prove this using formulas.

From formula (1), the value of q through r is inserted into the first part of the formula, we get: p = a / q = a / (b / r) = (a / b) * r. (2)

That is, according to the obtained formula (2), p is directly proportional to the value of r with a proportionality coefficient equal to (a / b), but in the particular case a = b = 1, then p = q.

Answer: p and r are directly proportional.