How to solve for Y when Y/20+Y * 100 = 40. I haven't done this in so long and am floored as to what to do when the unknown variable appears twice on the same side of the equation. Please help.

Question

jdoe0001 · Answer

$\bf \cfrac{y}{20}+y\cdot 100=40?$

phi · Answer

there are a few ways to tackle this.
one way is to multiply both sides (and all terms) by 20
as the first step.
can you try doing that ?

hlilly2413 · Answer

@jdoe0001 it's 20+Y under the Y then * 100 = 40. 
@phi So 20(y/20+y) and then 20(100) and 40(20)? sooo 20Y over 400+20Y *2000 = 800 would be the new equation?

phi · Answer

are you saying the problem is
$$ \frac{y}{20+y} \cdot 100 = 40 $$
?

hlilly2413 · Answer

Yes.

phi · Answer

in that case, we should start by multiplying both sides by (20+y)

hlilly2413 · Answer

Alright, I think I understand that by doing so it would cancel out the 20+y on the left. Do I also multiply the 100 by 20+y?

phi · Answer

when you multiply a fraction times a whole number you do
$$ \frac{2}{3} \cdot 4= \frac{2}{3} \cdot \frac{4}{1} = \frac{2\cdot 4}{3\cdot 1} $$
you multiply top times top and bottom times bottom

so the 100 is actually multiplying the top y

phi · Answer

you should get
$$ 100y= 40(y+20) $$

phi · Answer

now "distribute the 40"
that means 40 times each term inside the parens

hlilly2413 · Answer

Ok after I asked the question regarding the 100 I did not multiply it by 20 +Y. Thank you for the information there.  I did end up getting 100y = 800 + 40Y  and can def. take it from there. Thank you very much for your assistance @phi I appreciate it.