Question

How do I Make r the subject of this formula? t=12(s-r) divided by r

I cannot find a way to rearrange this formula; please help!

Any tips and hints are greatly appreciated
Thanks guys, Roman C :)

Answer 1

`r=(12s)/(t+12)`

Explanation:

`"we are given "t=(12(s-r))/r`

`"multiply both sides by "r`

`rt=cancel(r)xx(12(s-r))/cancel(r)`

`rt=12(s-r)larrcolor(blue)"distribute"`

`rt=12s-12r`

`"add "12r" to both sides"`

`rt+12r=12s`

`"take out "r" as a "color(blue)"common factor"`

`r(t+12)=12s`

`"divide both sides by "(t+12)`

`r=(12s)/(t+12)`

Answer 2

`r=(12s)/(t+12)`

Explanation:

Making `r` the subject of this formula just means we want to solve for `r` in terms of the other variables.

Right now, we have

`t=(12(s-r))/r`

We don't want `r` in the denominator, so let's multiply both sides by it to get

`rt=12(s-r)`

Distributing the `12` on the right gives us

`rt=12s-12r`

To solve for `r`, we want to get all of our `r` terms on one side. Let's add `12r` to both sides to get

`rt+12r=12s`

Both left side terms have an `r`, so we can factor that out.

`r(t+12)=12s`

Our last step would be to divide both sides by `t+12` to get

`r=(12s)/(t+12)`

Hope this helps!