Question

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

Answer 1

`p =4`

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\ (1)/(q)`

Convert to an equation

`p= k *(1)/(q)`

`p= (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= (k)/(q)`

`p = (540)/(135)`

`p =4`