Finding volume of a solution using %W/V

[Ace.]

Homework Statement

What volume of a 30% W/V hydrogen peroxide solution is required to prepare 425 mL of a 6.0% W/V solution?

Homework Equations

%w/v = (weight solute/volume solution) x 100%

The Attempt at a Solution

I'm not quite sure what to do because here I am given 2 percentages?
%w/v = (weight solute/volume solution) x 100%
Weight solute = (%w/v × volume solution)/100%

= (30% × 0.425 L)/100%​

= 0.1275 L​

Where to go from here and to apply this to the 6% solution?

 

[symbolipoint]

Homework Statement

What volume of a 30% W/V hydrogen peroxide solution is required to prepare 425 mL of a 6.0% W/V solution?

Homework Equations

%w/v = (weight solute/volume solution) x 100%

The Attempt at a Solution

I'm not quite sure what to do because here I am given 2 percentages?
%w/v = (weight solute/volume solution) x 100%
Weight solute = (%w/v × volume solution)/100%

= (30% × 0.425 L)/100%​

= 0.1275 L​

Where to go from here and to apply this to the 6% solution?

Biggest part of solving is to create the system of equations.

Let v = volume of stock solution, the 30%.
Let w = volume of just the water for dilution, 0% solute.
You want total resulting solution 425 ml.
425 = w + v.
$\[ v + w = 425\,ml \]$

You are taking v ml. of stock 30% and diluting it to get 6%. Using decimal fractions instead of percent, you setup a ratio relationship:
((0.30)v)/(v+w) = 0.06
$\[ \frac{{0.30v}}{{v + w}} = 0.06 \]$

Two unknown numbers and two equations. Solve.