Question

If p varies inversely as q, and p = 7 when q = 3, find p when $q = 2\dfrac{1}{3}$.

Answer 1

Hint: In this question as $p$ varies inversely as $q$ then let $p = \dfrac{k}{q}$, where $k$ is a constant. Use this concept to solve the question.

Complete step-by-step answer:
Given that $p$ varies inversely as $q$ then we can say that,
$p = \dfrac{k}{q}$, where $k$ is a constant.
We have been given in the question that –
As $p = 7$ when $q = 3$, so this will satisfy the equation $p = \dfrac{k}{q}$,
Therefore, keeping $p = 7$ and $q = 3$ in $p = \dfrac{k}{q}$, we get-
$
  7 = \dfrac{k}{3} \\
   \Rightarrow k = 21 \\
 $
Now put the value of $k$ in $p = \dfrac{k}{q}$, we get-
$p = \dfrac{{21}}{q}$
Now we have to find the value of $p$, when the value of $q = 2\dfrac{1}{3}$.
So, substituting these values in $p = \dfrac{{21}}{q}$, we get-
$p = \dfrac{{21}}{{2\dfrac{1}{3}}} = \dfrac{{21}}{{\dfrac{7}{3}}} = \dfrac{{21}}{7} \times 3 = 9$
Hence, after solving the question, we get the value of $p = 9$.

Note: Whenever such types of questions appear, then always form an equation according to the relation between the two given variables, and then solve by substituting the values of the variables which are provided in the question and then you can reach the solution easily.