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The variable, y, varies directly with x. if y = 18 when x = 13, what is y when x = 63?

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When we talk about direct variation we mean the following relationship between variables:


y=kx

where "k" is a constant. We must determine the value of this constant. To do that, we use the fact that when y = 18, x = 13, we replace that in the relationship:


18=k(13)

Now we solve for "k", dividing both sides by 13, like this:


(18)/(13)=k

solving we get;


k=1.38

We replace this value in the relationship:


y=1.38x

Now we are asked the value of "y", when "x = 63", we replace x = 63 in the relationship, we get:


\begin{gathered} y=1.38x \\ y=1.38(63) \end{gathered}

solving we get;


y=87.23

Therefore, y = 87.23 when x = 63

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