Question

Question #2e00d

Answer 1

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.