Question

A hair dye is made by blending 7% hydrogen peroxide solution and a 4% hydrogen peroxide solution. How many milliliter of each are used to make a 300 mL solution that is 5% hydrogen peroxide?

Answer 1

To create 300 mL of a 5% hydrogen peroxide solution, one needs 100 mL of a 7% solution and 200 mL of a 4% solution. This is found by solving a system of linear equations for the volumes of each solution needed.

Step-by-step explanation:

To solve the problem of blending two hydrogen peroxide solutions to achieve a specific concentration, we can use a system of linear equations. We want to mix a 7% hydrogen peroxide solution with a 4% hydrogen peroxide solution to obtain 300 mL of a 5% hydrogen peroxide solution.

The system of equations is based on the principle that the amount of pure hydrogen peroxide in the final solution is the sum of the amounts in the individual solutions before mixing.

Let x be the volume of the 7% solution and y be the volume of the 4% solution we need to mix. Two equations can be formulated as follows:

• Equation for volume: x + y = 300 (since the total volume is 300 mL).
• Equation for concentration: 0.07x + 0.04y = 0.05 × 300 (since the final solution should be 5% hydrogen peroxide).

By solving this system of equations, we find:

1. Multiplying the second equation by 100 to eliminate the decimals gives: 7x + 4y = 1500.
2. Subtract the first equation multiplied by 4 from the modified second equation to eliminate y: 7x + 4y - 4(×x + y) = 1500 - 4(300).
3. This simplifies to 3x = 300 and subsequently x = 100.
4. Substituting x = 100 into the first equation gives y = 200.

Therefore, to make a 300 mL solution that is 5% hydrogen peroxide, one would need 100 mL of the 7% solution and 200 mL of the 4% solution.

Answer 2

i think its 30 mL.......