SOLUTION: How to calculate a 3% solution (of 1000mls) from a 93% stock (of 100mls). I have tried the method... {{{ C1 x V1 = C2 x V2 . V1 = (C2 x V2) / C1 = ? }}} but am a little confus

Question 829840: How to calculate a 3% solution (of 1000mls) from a 93% stock (of 100mls).
I have tried the method...

but am a little confused and not really sure if it the formula that I ought to be using.
C1 = 93% [x100] = 0.93
V1 = 100mls
C2 = ? [I don't know what goes here]
V2 = 1000mls
V1 = (V2 x C2) / C1 = ? 100ml = (1000mls x C2) / 100mls = ?
I get stuck at C2! What is this meant to be? Where do I get the number from?

Is this even the right formula for me?!
I have a stock that is a 93% solution, but I have 1000mls of water that I need to be at 3%.
Hope you can help or confuse me!
Thank you
:)
Mariana

Found 2 solutions by TimothyLamb, josgarithmetic:
Answer by TimothyLamb(4379) (Show Source): You can put this solution on YOUR website!
---
I'm assuming that the solvent is pure water, so the answer is clear.
The answer is the same regardless of the solvent.
---
x = volume of pure water
y = volume of 93% stock solution
---
0x + 93y = 3(x + y)
x + y = 1000
---
put the system of linear equations into standard form:
---
93y = 3x + 3y
x + y = 1000
---
3x - 90y = 0
x + y = 1000
---
copy and paste the above linear system in standard form into this matrix-method solver:
https://sooeet.com/math/system-of-linear-equations-solver.php
---
answer:
x = volume of pure water = 967.742 ml
y = volume of 93% stock solution = 32.258 ml
---
check total volume = 967.742 + 32.258 = 1000.000 ml
---
Solve and graph linear equations:
https://sooeet.com/math/linear-equation-solver.php
---
Solve quadratic equations, quadratic formula:
https://sooeet.com/math/quadratic-formula-solver.php
---
Solve systems of linear equations up to 6-equations 6-variables:
https://sooeet.com/math/system-of-linear-equations-solver.php

Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
One could change the variable names like this and use, as you have chosen, to use decimal fractions instead of percents:

C = 0.93 for the stock concentration
T = 0.03 for the Target concentration
u = ml. volume of the stock solution to add or use
V = 1000 ml. volume of your target, desired solution

Amount of solute from stock will be the amount of solute of your desired solution. Your initial idea was correct, and using the variable names chosen in this posting, you would write:

'
Solve for u.

'
You wanted a known V, volume of the finished solution, 1000 ml. You are adding the quantity u to some amount of solvent (probably water, but it would be whatever solvent you are using).
'
What is u?

mililiters
THAT u is what quantity you add to water, and the amount of water, avoiding further variable usage, is ml. or the quantity enough to make up to your 1000 ml. of solution.
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