OpenStudy (hlilly2413):

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.

2 years ago
OpenStudy (jdoe0001):

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

2 years ago
OpenStudy (phi):

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 ?

2 years ago
OpenStudy (hlilly2413):

@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?

2 years ago
OpenStudy (phi):

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

2 years ago
OpenStudy (hlilly2413):

Yes.

2 years ago
OpenStudy (phi):

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

2 years ago
OpenStudy (hlilly2413):

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?

2 years ago
OpenStudy (phi):

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

2 years ago
OpenStudy (phi):

you should get \[ 100y= 40(y+20) \]

2 years ago
OpenStudy (phi):

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

2 years ago
OpenStudy (hlilly2413):

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.

2 years ago