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 :)

2 Answers
Jul 4, 2018

#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)#

Jul 4, 2018

#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!