Question

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 1

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:

$C=\frac{x+0.1(500)}{x+500}$

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:

$0.28=\frac{x+0.1(500)}{x+500}$

and now we can solve for x. We can start by multiplying both sides of the equation by (x+500) so we get:

$0.28(x+500)=x+0.1(500)$

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:

$0.28x+140=x+50$

so now we can subtract an x from both sides so we get:

$0.28-x+140=x-x+50$

which yields:

$-0.72x+140=50$

Now, we can subtract a 140 from both sides, so we get:

$-0.72x+140-140=50-140$

Which yields:

$-0.72x=-90$

and finally we can divide both sides into -0.72 so we get:

$\frac{-0.72x}{-0.72}=\frac{-90}{-0.72}$

$x=125lt$

So we need to add 125 litters of pure peroxide to produce a new product that is 28% peroxide.