A company wants to increase the 10% peroxide content of its product by adding pure peroxide (100% peroxide). If x liters of pure peroxide are added to 500 liters of its 10% solution,the concentration, C, of the new mixture is given by C = x+0.1(500) / x+500. How many liters of pure peroxide should be added to produce a new product that is 28% peroxide?

Answer:There should be 125 litters of pure peroxide added to produce a new product that is 28% peroxide.Step-by-step explanation:The problem provides us with an equation we can use to find the concentration C of the new mixture, which is:[tex]C=\frac{x+0.1(500)}{x+500}[/tex]which will give us the concentration C as a decimal number.We are interested in getting a concentration of 28%, which is written as 0.28 in decimal form. This is our C.Now we can substitute it into the equation:[tex]0.28=\frac{x+0.1(500)}{x+500}[/tex]and now we can solve for x. We can start by multiplying both sides of the equation by (x+500) so we get:[tex]0.28(x+500)=x+0.1(500)[/tex]Next, we can distribute dhe 0.28 on the left of the equation and we can also multiply the 0.1(500) on the right side, so we get:[tex]0.28x+140=x+50[/tex]so now we can subtract an x from both sides so we get:[tex]0.28-x+140=x-x+50[/tex]which yields:[tex]-0.72x+140=50[/tex]Now, we can subtract a 140 from both sides, so we get:[tex]-0.72x+140-140=50-140[/tex]Which yields:[tex]-0.72x=-90[/tex]and finally we can divide both sides into -0.72 so we get:[tex]\frac{-0.72x}{-0.72}=\frac{-90}{-0.72}[/tex][tex]x=125lt[/tex]So we need to add 125 litters of pure peroxide to produce a new product that is 28% peroxide.