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The value of y varies inversely as \(\sqrt x \) and when x=24, y=15. What is x when y = 3?

 Jun 23, 2020
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Since y and \(\sqrt{x}\) are inversely proportional, this means that \(y\sqrt{x}=k\) for some constant k. Substituting the given values, when x=24 and y=15, we find that \(15\sqrt{24}=k\). Therefore, when y=3, we can solve for x:

\(\begin{align*} 3\cdot\sqrt{x}&=15\sqrt{24}\\ \Rightarrow\qquad 9x=5400\\ \Rightarrow\qquad x&=\boxed{600} \end{align*}\)

 Jun 23, 2020

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