If y varies inversely as x, and the two values of x are in the ratio 3:2, what is the ratio of the corresponding values of y?

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If y varies inversely as x, and the two values of x are in the ratio 3:2, what is the ratio of the corresponding values of y?

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Answer 1 · 2017-04-13T09:25:14

The question is not clear about all the relationships. So I have guessed. I am not convinced that I have interpreted you question correctly.

Explanation:

$If y varies inversely as x: \to y = \frac{k}{x}$ $color(blue)("If y varies inversely as x: "->)y=k/x$ where $k$ $k$ is some constant
$and the two values of x: \to y_{1} = \frac{k}{x_{1}} y_{2} = \frac{k}{x_{2}}$ $color(blue)("and the two values of x: ")-> y_1=k/x_1" "y_2=k/x_2$

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$are in the ratio of 3:2 \to building the relationship:$ $color(blue)("are in the ratio of 3:2 ")->color(brown)(" building the relationship:")$

Not that 3 parts and 2 parts make a total of 3+2 parts=5 parts

Let $a$ $a$ be some constant. Then I choose $a$ $a$ such that

$\frac{3}{5} a = x_{1} and \frac{2}{5} a = x_{2}$ $3/5a=x_1 and 2/5a=x_2$

$\Rightarrow y_{1} = \frac{k}{\frac{3}{5} a} and y_{2} = \frac{k}{\frac{2}{5} a}$ $=>y_1=k/(3/5a) and y_2=k/(2/5a)$
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$What is the ratio of the corresponding values of y$ $color(blue)("What is the ratio of the corresponding values of y")$

I chose the order of the ratio to be: $y_{1} : y_{2} \to \frac{y_{1}}{y_{2}}$ $" "y_1:y_2->y_1/y_2$

So we have $\frac{y_{1}}{y_{2}} \to \frac{k}{\frac{3}{5} a} \div \frac{k}{\frac{2}{5} a}$ $y_1/y_2-> k/(3/5a) -: k/(2/5a)$

$\frac{5 k}{3 a} \div \frac{5 k}{2 a} = \frac{5 k}{3 a} \times \frac{2 a}{5 k} = \frac{2}{3} \to 2 : 3$ $(5k)/(3a)-:(5k)/(2a)" " =" "(5k)/(3a)xx(2a)/(5k) = 2/3 ->2:3$

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If y varies inversely as x, and the two values of x are in the ratio 3:2, what is the ratio of the corresponding values of y?

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