If an increase in one quantity results in a decrease in the other in a way to keep the product of their respective values constant, the two are said to vary ____ with one another.

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Detailed Solution

If an increase in one quantity results in a decrease in the other in a way to keep the product of their respective values constant, the two are said to vary inversely with one another.
We know that two variables

x and y

are said to be inversely proportional if and only if they are directly proportional to one another's reciprocal. If

x and y

are two variables in inverse variations, then

x ∝ 1 y ⇒ x = k 1 y ⇒ x = k y,        where k is proportianality constant ⇒ x y = k .... (1)

Equation (1) shows that the two quantities

x and y

are said to be inversely proportional to each other when their product of corresponding values remains constant.
Therefore, if an increase in one quantity results in a decrease in the other in a way to keep the product of their respective values constant, the two are said to vary inversely with one another.

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