A company has 35% and 3% hydrogen peroxide solutions. They need an 8L container with a 12% concentration of hydrogen peroxide. How much of the 3% hydrogen peroxide solution should they include in the container? L

Define the amount of 3% hydrogen peroxide: Let x be the amount of 3% hydrogen peroxide solution that needs to be added. Then, the amount of 35% hydrogen peroxide solution to be added would be (8 - x) liters, because the total volume of the solution needs to be 8 liters.Set up the equation for the final concentration: Set up the equation based on the concentration of hydrogen peroxide in each solution and the desired final concentration. The total amount of pure hydrogen peroxide in the final solution should be equal to the sum of the amounts in the individual solutions before mixing. Equation: (0.03 * x) + (0.35 * (8 - x)) = 0.12 * 8Distribute and simplify the equation: Distribute the concentrations and simplify the equation. 0.03x + 2.8 - 0.35x = 0.96Combine like terms and solve for x: Combine like terms and solve for x. -0.32x + 2.8 = 0.96Isolate the term with x: Subtract 2.8 from both sides of the equation to isolate the term with x. -0.32x = 0.96 - 2.8 -0.32x = -1.84Solve for x: Divide both sides by -0.32 to solve for x. x = -1.84 / -0.32 x = 5.75

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A company has
35% and
3% hydrogen peroxide solutions. They need an
8L container with a
12% concentration of hydrogen peroxide.
How much of the
3% hydrogen peroxide solution should they include in the container?
L

A company has $35 \%$ and $3 \%$ hydrogen peroxide solutions. They need an $8 \mathrm{~L}$ container with a $12 \%$ concentration of hydrogen peroxide. $\newline$ How much of the $3 \%$ hydrogen peroxide solution should they include in the container? $\newline$ L

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Q. A company has

35 \%

and

3 \%

hydrogen peroxide solutions. They need an

8 \mathrm{~L}

container with a

12 \%

concentration of hydrogen peroxide.

\newline

How much of the

3 \%

hydrogen peroxide solution should they include in the container?

\newline

Define the amount of $3\%$ hydrogen peroxide: Let $x$ be the amount of $3\%$ hydrogen peroxide solution that needs to be added. Then, the amount of $35\%$ hydrogen peroxide solution to be added would be $(8 - x)$ liters, because the total volume of the solution needs to be $8$ liters.
Set up the equation for the final concentration: Set up the equation based on the concentration of hydrogen peroxide in each solution and the desired final concentration. The total amount of pure hydrogen peroxide in the final solution should be equal to the sum of the amounts in the individual solutions before mixing. $\newline$ Equation: $(0.03 \times x) + (0.35 \times (8 - x)) = 0.12 \times 8$
Distribute and simplify the equation: Distribute the concentrations and simplify the equation. $\newline$ $0.03x + 2.8 - 0.35x = 0.96$
Combine like terms and solve for x: Combine like terms and solve for x. $-0.32x + 2.8 = 0.96$
Isolate the term with x: Subtract $2.8$ from both sides of the equation to isolate the term with $x$ . $\newline$ $-0.32x = 0.96 - 2.8$ $\newline$ $-0.32x = -1.84$
Solve for x: Divide both sides by $-0.32$ to solve for $x$ . $x = \frac{-1.84}{-0.32}$ $x = 5.75$