Question

Suppose p and q vary inversely and p=14 when q=4. Find p when q=8.

Answer 1

If p and q vary inversely, the value of p when q = 8 is:

• p = 7

Explanation:

If p and q vary inversely then:

`\boxed{p \propto (1)/(q)\implies p=(k)/(q)}`

where k is a constant to be found.

If p = 14 when q = 4, substitute these values into the equation and solve for k:

`\implies 14=(k)/(4)`

`\implies 14 \cdot 4=(k)/(4) \cdot 4`

`\implies k=56`

Substitute the found value of the constant k into the equation to create an equation for p in terms of q:

`\boxed{p=(56)/(q)}`

To find the value of p when q = 8, substitute q = 8 into the equation:

`\implies p=(56)/(8)`

`\implies p=7`

Therefore, the value of p when q = 8 is:

• p = 7