Question

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

Answer 1

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