If y varies inversely as x, and y=7 when x=6, what is y when x=3?

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If y varies inversely as x, and y=7 when x=6, what is y when x=3?

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Answer 1 · 2016-07-14T12:36:06

$y = 14$ $y=14$

Explanation:

$y \propto \frac{1}{x} \Rightarrow y = \frac{k}{x}$ $y prop 1/x implies y = k/x$ where k is a constant of proportionality.

$y_{1} = 7, x_{1} = 6$ $y_1 = 7, x_1 = 6$
$y_{2} = ?, x_{2} = 3$ $y_2 = ?, x_2 = 3$

$\frac{y_{2}}{y_{1}} = \frac{\frac{k}{x_{2}}}{\frac{k}{x_{1}}} = \frac{k}{x_{2}} \cdot \frac{x_{1}}{k} = \frac{x_{1}}{x_{2}}$ $(y_2)/(y_1) = (k/x_2)/(k/x_1) = k/x_2*x_1/k = x_1/x_2$

$therefore y_2 = y_1*x_1/x_2$

$y_2 = 7*6/3 = 7*2 = 14$

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If y varies inversely as x, and y=7 when x=6, what is y when x=3?

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