GreenlightTestPrep wrote:
How many liters of a solution that is 15 percent salt must be added to 5 liters of a solution that is 8 percent salt so that the resulting solution is 10 percent salt?
When solving mixture questions, it can be useful to sketch the solutions with the ingredients SEPARATED.
8% of 5 liters = 0.4 liters. So, the original mixture contains
0.4 liters of salt
Let x = the volume (in liters) of 15% solution required
So, this solution contains
0.15x liters of salt
We get:
We want the resulting solution to be 10% salt.
In other words, we want: \(\frac{0.4 + 0.15x}{5+x}=\frac{10}{100}\) (aka 10%)
Simplify: \(\frac{0.4 + 0.15x}{5+x}=\frac{1}{10}\)
Cross multiply: \((10)(0.4 + 0.15x) = 5+x\)
Expand: \(4 + 1.5x = 5+x\)
Solve: \(x = 2\)
Answer: 2
Cheers,
Brent