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.
