Question

The variables $ x $ and $ y $ vary inversely. How do you write an equation that relates $ x $ and $ y $ given $ x=15 $ , $ y=5 $ ?

Answer 1

Hint: In the problem, they have mentioned that the variables $ x $ and $ y $ vary inversely. So mathematically we can write the product of the variables $ x $ and $ y $ is always a constant. Here we will assume the constant as $ k $ and write the equation. Now we have the values of $ x $ and $ y $, so we will substitute those values in the obtained equation and calculate the value of constant $ k $. After getting the value of $ k $ we will write the final equation.

Complete step by step answer:
Given that, The variables $ x $ and $ y $ vary inversely.
We know that if any two variables vary inversely, then the product of those variables should be always a constant. So, the product of the variables $ x $ and $ y $ is always a constant.
 $ \Rightarrow x\times y= $ constant.
Assuming the constant as $ k $ and substituting this value in the above equation, then we will get
 $ \Rightarrow x\times y=k...\left( \text{i} \right) $
In the problem we have the values of $ x $ and $ y $ as $ x=15 $ , $ y=5 $ . Substituting these values in the above equation, then we will get
 $ \begin{align}
  & \Rightarrow 15\times 5=k \\
 & \Rightarrow k=75 \\
\end{align} $
Substituting the value of $ k $ in the equation $ \left( \text{i} \right) $ , then we will get
 $ xy=75 $
Hence the required equation is $ xy=75 $ .

Note:
In the problem, they have only asked to calculate the equation or relation between the variables $ x $ and $ y $. But in some cases, they may ask to calculate the value of $ x $ for the given $ y $ value or vice versa. Then we will use the obtained relation and substitute the given value either $ x $ or $ y $ and calculate the value of a remaining variable.