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

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Weighted averages: word problems

Full solution

Q. A company has

35\%

and

3\%

hydrogen peroxide solutions. They need an

8\text{L}

container with a

12\%

concentration of hydrogen peroxide. How much of the

3\%

hydrogen peroxide solution should they include in the container?

Define variables: Let $x$ be the amount of $3\%$ solution and $(8 - x)$ be the amount of $35\%$ solution.
Set up equation: Set up the equation: $0.03x + 0.35(8 - x) = 0.12 \times 8$ .
Distribute and simplify: Distribute and simplify: $0.03x + 2.8 - 0.35x = 0.96$ .
Combine like terms: Combine like terms: $-0.32x + 2.8 = 0.96$ .
Subtract and simplify: Subtract $2.8$ from both sides: $-0.32x = 0.96 - 2.8$ .
Calculate right side: Calculate the right side: $-0.32x = -1.84$ .
Solve for x: Divide by $-0.32$ to solve for x: $x = \frac{-1.84}{-0.32}$ .
Calculate x: Calculate $x$ : $x = 5.75$ .

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