Question

x varies directly as y, and x = 153 when y = 9. How do you find x when y = 13?

Answer 1

Hint: Assume that y is directly proportional to x. Remove the proportionality sign and assume a constant ‘k’ in place of that. Now, substitute the value of x and y given in the question and find the value of constant ‘k’. Substitute this value of k in the relation y = kx to find the actual relation between x and y. Now, substitute y = 13 and solve for the value of x to get the answer.

Complete step by step answer:
Here, we have been provided with the information that x is varying directly as y. So, first we need to find the actual relation between x and y to proceed further.
According to the question, we have,
\[\Rightarrow y\propto x\]
Now, we know that when the proportionality sign is removed, a constant is assumed in place of that. Here, we are assuming the required constant as K. So, we have,
\[\Rightarrow y=Kx\] -(1)
Also, we have been provided that when x = 153 then y = 9. So, substituting these values of x and y in equation (1), we get,
\[\begin{align}
  & \Rightarrow 9=K\times 153 \\
 & \Rightarrow K=\dfrac{9}{153} \\
\end{align}\]
Cancelling the common factors, we get,
\[\Rightarrow K=\dfrac{1}{17}\]
So, the value of proportionality constant is \[K=\dfrac{1}{17}\], therefore the actual relation between x and y can be given by substituting this obtained value of K in \[y=Kx\], so we have,
\[\Rightarrow y=\dfrac{x}{17}\]
Now, we are asked to determine the value of x when the value of y becomes 13, so substituting y = 13 in the above obtained relation, we get,
\[\Rightarrow 13=\dfrac{x}{17}\]
By cross – multiplying, we get,
\[\begin{align}
  & \Rightarrow 13\times 17=x \\
 & \Rightarrow x=221 \\
\end{align}\]

Hence, x = 221 is our answer.

Note: One may note that at the initial step of the above solution we have assumed the relation between x and y as \[y=Kx\], you may also assume it as \[x=Ky\]. In this case when you will substitute the given values of x and y then you will obtain K = 17. This does not mean that we are getting a wrong relation because we can change \[x=17y\] into \[y=\dfrac{1}{17}x\]. Both are the same thing. Remember that, for solving the second part of the question we need to find the value of ‘K’ just as we did above.