The Solution:
Given that p and q are inversely related, we have that:
[tex]p\propto\frac{1}{q}[/tex]
This means that:
[tex]\begin{gathered} p=\frac{1}{q}\times k \\ \\ p=\frac{k}{q} \\ \\ \text{ Where k=constant of variation.} \end{gathered}[/tex]
Given the initial condition (or values) that p =30 when q = 25.
Substituting these values in the relation above, we get
[tex]30=\frac{k}{25}[/tex]
Cross multiplying, we get
[tex]k=30\times25=750[/tex]
So, the formula connecting p and q is obtained as
[tex]p=\frac{750}{q}[/tex]
We are asked to find the value of q when p = 50.
Substitute 50 for p in the formula connecting p and q.
[tex]50=\frac{750}{q}[/tex]
Cross multiplying, we get
[tex]50q=750[/tex]
Dividing both sides by 50, we get
[tex]\begin{gathered} \frac{50q}{50}=\frac{750}{50} \\ \\ q=15 \end{gathered}[/tex]
Therefore,
