Question

If p and q vary inversely and p is 2 when q is 21, determine q when p is equal to 6.

Answer 1

`q = 7`

Explanation:

Given

`p\ \alpha\ (1)/(q)` --- inverse variation

`p =2; q = 21`

Required

Find q when
`p = 6`

`p\ \alpha\ (1)/(q)`

This becomes

`p = (k)/(q)`

Where k is the constant of variation.

Make k the subject

`k = p * q`

Substitute
`p =2; q = 21`

`k = 2 * 21`

`k =42`

When
`p = 6`, we have:

`p = (k)/(q)`

`6 = (42)/(q)\\`

Make q the subject

`q = (42)/(6)`

`q = 7`