Question

It is given that p varies inversely as q. If p = 12 and q = 45 find p, if q is 135.

Answer 1

Answer:

$p =4$

Step-by-step explanation:

Given

Variation: Inversely

$p = 12$ when $q = 45$

Required

Determine p when $q = 135$

First, we need to determine the relationship between p and q

Since, it is an inverse variation.

The relationship is:

$p\ \alpha\ \frac{1}{q}$

Convert to an equation

$p= k *\frac{1}{q}$

$p= \frac{k}{q}$

Where k = constant of variation

Make k the subject

$k = p * q$

When $p = 12$ and $q = 45$

$k = 12 * 45$

$k = 540$

To solve for p when q = 135

Substitute 135 for q and 540 for k in $p= \frac{k}{q}$

$p = \frac{540}{135}$

$p =4$