MATH SOLVE

2 months ago

Q:
# A 4% peroxide solution is mixed with a 10% peroxide solution, resulting in 100 L of an 8% solution. The table shows the amount of each solution used in the mixture.What is the value of z in the table?

Accepted Solution

A:

Answer:[tex]\textbf{There are }33\tfrac{1}{3}\textbf{ liters of the 4}\%\textbf{ solution and }66\tfrac{2}{3}\textbf{ liters of the 10}\%\textbf{ solution.}[/tex]Step-by-step explanation:Let x represent the amount of 4% solution and y represent the amount of 10% solution.⇒ x + y = 100 ..................(1)x liters of the 4% solution gives us the expression 0.04·xy liters of the 10% solution gives us the expression 0.10·y100 L of the 8% solution gives us 0.08 × (100) = 8⇒ 0.04·x + 0.10·y = 8 ...........(2)This gives us the system of equations (1) and (2)To solve this, we will use substitution.Substituting x = 100 - y from equation (1) into equation (2). We get,[tex]y = 66\tfrac{2}{3}[/tex]Substitute this value of y into the first equation:[tex]x + 66\tfrac{2}{3} = 100\\\\\text{Subtract }66\tfrac{2}{3}\text{ from each side :}\\\\\implies x = 33\tfrac{1}{3}\\\\\textbf{Hence,There are }33\tfrac{1}{3}\textbf{ liters of the 4}\%\textbf{ solution and }66\tfrac{2}{3}\textbf{ liters of the 10}\%\textbf{ solution.}[/tex]