Question #2e00d

1 Answer
Nov 3, 2017

5 L

Explanation:

Let's call the number of liters we'll need of the 10% solution n. Adding 10 L of the 4% solution, we end up with n+10 L of the desired 6% solution. Using those expressions, let's take a look at our problem statement in English, and then translate that into a mathematical statement.

Here's our statement in English:

"Mixing n L of 10% solution and 10 L of 4% solution yields n+10 L of 6% solution."

To turn that into math:

  • We can rewrite "Mixing n L of 10% solution and 10 L of 4% solution" as an expression adding n*0.1 (n L of 10% solution) and 10*0.04 (10 L of 4% solution), obtaining the expression n*0.1+10*0.04
  • This expression will "yield", or be equal to, (n+10)*0.06 (n+10 L of 6% solution).

Putting that all together, we get the equation n*0.1+10*0.04=(n+10)*0.06, which we can then solve for n. Let's do that.

First, we can simplify 10*0.04 on the left side to get 0.4, and we can distribute on the right:

n*0.1+0.4=n*0.06+10*0.06

Let's multiply 10*0.06 on the right side and rearrange n*0.1 and n*0.06 to make the notation a little more familiar:

0.1n+0.4=0.06n+0.6

Subtract 0.4 from both sides:

0.1n=0.06n+0.2

Subtract 0.06n from both sides:

0.04n=0.2

And divide both sides by 0.04:

n=5

So, we'll need 5 L of 10% solution to give us our desired 6% concentration.