Question

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?

Answer 1

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:

`color(blue)("If y varies inversely as x: "->)y=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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`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` be some constant. Then I choose `a` such that

`3/5a=x_1 and 2/5a=x_2`

`=>y_1=k/(3/5a) and y_2=k/(2/5a)`
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`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->y_1/y_2`

So we have `y_1/y_2-> k/(3/5a) -: k/(2/5a)`

`(5k)/(3a)-:(5k)/(2a)" " =" "(5k)/(3a)xx(2a)/(5k) = 2/3 ->2:3`