Question

If y varies with x, and if y = -18 when x=6, how do you find x when y = 6?

Answer 1

Hint: Start the solution by defining what exactly the meaning of y varies with x. The term usually means that their ratio remains the same. Hence first calculate the ratio of x and y from the given values of x and y and then compare it to the other set of information to get the missing value.

Complete step by step solution:
Observing from the start the question says that y varies with x. The simple meaning of this statement is that if the value of x increases, the value of y increases. Similarly, if the value of x decreases the value of y will also decrease. That is the ratio between them always remains the same.
So as given in the question, they have already given us the values of x and y first. We will first find the ratio of x and y i.e. $ \dfrac{x}{y} $ . Now since y varies x, the ratio has to be the same. Hence for the next given value of y we have to find the value of x such that their ratio remains the same as that of the first ratio.
So, $ \dfrac{x}{y} = \dfrac{6}{{ - 18}} = - \dfrac{1}{3} $ is the first ratio. This ratio should be the same for the second set of values.
Hence,
 $
  \dfrac{x}{6} = \dfrac{{ - 1}}{3} \\
   \Rightarrow x = - 2 \;
  $
Hence the value of x = -2 respectively.
So, the correct answer is “x = -2”.

Note: In the question it is given it is given as y varies with x. it can also be said as y varies directly as x or y is directly proportional to x or y varies proportionally to x which are one and the same. The meaning changes when it is given as y is inversely proportional to x . In this case when the values of x increases the value of y decreases and vice versa.