# 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?

Apr 13, 2017

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:

$\textcolor{b l u e}{\text{If y varies inversely as x: } \to} y = \frac{k}{x}$ where $k$ is some constant
color(blue)("and the two values of x: ")-> y_1=k/x_1" "y_2=k/x_2

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$\textcolor{b l u e}{\text{are in the ratio of 3:2 ")->color(brown)(" building the relationship:}}$

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

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

$\frac{3}{5} a = {x}_{1} \mathmr{and} \frac{2}{5} a = {x}_{2}$

$\implies {y}_{1} = \frac{k}{\frac{3}{5} a} \mathmr{and} {y}_{2} = \frac{k}{\frac{2}{5} a}$
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$\textcolor{b l u e}{\text{What is the ratio of the corresponding values of y}}$

I chose the order of the ratio to be: $\text{ } {y}_{1} : {y}_{2} \to {y}_{1} / {y}_{2}$

So we have ${y}_{1} / {y}_{2} \to \frac{k}{\frac{3}{5} a} \div \frac{k}{\frac{2}{5} a}$

$\frac{5 k}{3 a} \div \frac{5 k}{2 a} \text{ " =" } \frac{5 k}{3 a} \times \frac{2 a}{5 k} = \frac{2}{3} \to 2 : 3$