A beautician makes a 14.3% peroxide solution by mixing some 5% peroxide solution with some 20% peroxide solution. How much 5% peroxide solution does the beautician use to make 109 ounces of 14.3% peroxide solution?

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KannonR658265 KannonR658265

29-10-2022
Mathematics

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A beautician makes a 14.3% peroxide solution by mixing some 5% peroxide solution with some 20% peroxide solution. How much 5% peroxide solution does the beautician use to make 109 ounces of 14.3% peroxide solution?

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JananiG615851 JananiG615851 · Answer 1 · 2022-10-29T03:57:43+02:00

The question is first given in percentages. However, the requirement is to find the actual weight of the substance.

Given the value of the weight of a single fraction in the combination, we can get the weights of the other samples.

We'll thus have:

[tex]0.05x+0.2(109-x)=0.143(109)[/tex]

Next, we solve for x

[tex]\begin{gathered} 0.05x+21.8-0.2x=15.587 \\ 0.05x-0.2x=15.587-21.8 \\ -0.15x=-6.213 \\ \text{Divide both sides by -0.15} \\ x=41.42 \end{gathered}[/tex]

ANS = 41.42