Percent Mix Help!!!

[TylerLinden]

The problem is:

"Hermione is brewing Polyjuice potion in the girl’s bathroom. She can use a pewter cauldron (30 gallons),a brass cauldron (45 gallons) or a copper cauldron (10 gallons). The ingredients to brew this potion areas follows:

Lacewing Flies, Fluxweed, Knotgrass, Leeches, Horn of Bicorn, Skin of Boomslang, Slytherin student’shair.

Currently Hermione’s concentration of Lacewing Flies is 14%. A proper brew has a Lacewing Fly concentration of 37%. If Hermione is brewing in the pewter cauldron and her original blend was 9 3/4 gallons, how many gallons of pure Lacewing Fly must be added to reach the proper concentration?"

I've done problems like this one before. I usually use a chart to set this one up but so far nothing's working. I'm not exactly sure where the X goes and I'm just generally stumped. I don't want you to solve the problem for me, just help me set it up into something solve-able. Thanks!

 

[TylerLinden]

Still not sure.

Well, start by rewriting (that professor of yours is a clown?!):

9.75 gallons of a water and salt mixture has 14% salt.
How many gallons of salt must be added so the mixture is 37%?

9.75 : 14
S : 100
======
9.75+S : 37

I'm still not exactly sure what you did there. Where did the 100 come from? Why are you putting it into ratios? Please give more detail. In class we've been putting things into charts like this: [this chart is from a different problem]

	Gallons	% Salt	Amount
Original	240	.03	7.2
Water	x	0	0
New Mix	240-x	.05	.05(240-x)

 

[Dale10101]

A not S

I'll change my salt to 100% Alcohol!
9.75 : 14
A : 100 ..................A gallons of 100% alcohol (A) is added
========
9.75+A : 37

[14(9.75) + 100A] / (9.75 + S) = 37 (same as using .14, 1.0 and .37)

Solve for A to get 3.5595....gallons

So we went from 9.75 gallons of a 14% alcohol drink to ~13.31 gallons of a 37% alcohol drink:
take less time to get drunk!

That's the way I understand your problem...

I think Denis made a typo, shouldn't it be 9.75 + A instead of 9.75 + S in the equation denominator.

 

[soroban]

[Hello, TylerLinden!

Most of the information is irrelevant.

Hermione has 9.75 gallons of brew which is 14% Lacewing \(\displaystyle (L)\).
She want a mixture which 37% \(\displaystyle L\).
How many gallons of pure \(\displaystyle L \)must she add?

\(\displaystyle \begin{array}{c||c|c|c|} & \text{Gallons} & \%\,L & \text{Amount (L)} \\ \hline \text{Original} & 9.75 & 0.14 & 1.365 \\ \hline \text{Lacewing} & x & 1.00 & x \\ \hline \text{Mixture} & x+9.75 & 0.37 & 0.37(x+9.75) \\ \hline \end{array}\)


The equation is in the last column: .\(\displaystyle 1.365 + x \:=\:0.37(x+9.75)\)

 

[Dale10101]

Shhh-ure

Thanks Dale. Don't tell Subhotosh!

Nada.