solve for Cf please

[courtesy flush]

Hey, new guy here.

I hope you'll be kind enough to help me.

Formula I have:

Vl = Vh ( Ch - Cf ) / ( Cf - Cl )

Formula I need:

Cf = ??

Can you help me rearrange this formula to solve for Cf? I'm just an old guy trying to figure out the final concentration of a solution ( Cf ) after I mix two different concentration solutions together. Maybe if you could show your work too, I might be able to recall these algebraic things I've long forgotten. Then again, maybe not.

Thanks,
Courtesy flush

 

[Dr.Peterson]

Vl = Vh ( Ch - Cf ) / ( Cf - Cl )

We normally require you to show your work so we know where to help, but I'll show the first couple steps, since you're an old guy like me:

Vl = Vh (Ch - Cf ) / (Cf - Cl)​

Multiply by the denominator:

Vl (Cf - Cl) = Vh (Ch - Cf)​

Distribute:

Vl Cf - Vl Cl = Vh Ch - Vh Cf​

Now try to isolate Cf as usual. There's another potentially tricky step, but I want to give you a chance to see what you can remember!

 

[courtesy flush]

Now you're just messing with me. "Isolate Cf as usual" eh?

ok.

Vl Cf - Vl Cl = Vh Ch - Vh Cf

Vl Cf = Vh Ch - Vh Cf + Vl Cl

Vh Cf + Vl Cf = Vh Ch + Vl Cl

Cf ( Vh + Vl ) = Vh Ch + Vl Cl

Cf = ( Vh Ch + Vl Cl ) / (Vh + Vl).........................added parentheses

Did I do it?

 

[courtesy flush]

That took a long time to type and proof read.

 

[Dr.Peterson]

Now you're just messing with me. "Isolate Cf as usual" eh?

ok.

Vl Cf - Vl Cl = Vh Ch - Vh Cf
Vl Cf = Vh Ch - Vh Cf + Vl Cl
Vh Cf + Vl Cf = Vh Ch + Vl Cl
Cf ( Vh + Vl ) = Vh Ch + Vl Cl
Cf = ( Vh Ch + Vl Cl ) / Vh + Vl

Did I do it?

Good -- I thought you could do it!

I'll just add necessary parentheses at the end: Cf = (Vh Ch + Vl Cl) / (Vh + Vl)

 

[Dr.Peterson]

Can someone help how to answer a new topic ??
What am I doing wrong?
Please help.
Yours faithfully.

Go to Forums, pick a forum (e.g. Beginning Algebra), and click "Post Thread" in the upper right.

I can't say what you are doing wrong without knowing what you are doing.

 

[JeffM]

I can't say what you are doing wrong without knowing what you are doing.

Why not? My wife is an expert at it.

 

[Deleted member 4993]

Why not? My wife is an expert at it.

I must have married your sister-in-law. It's genetics.......