Question

for a particular experiment you need 5 liters of a 10% solution. you find 7% and 12% solution on the shelves. How much of the 7% solution should you mix with the appropraite amount of the 12% solution to get 5liters of a 10% solution.

Answer 1

Let \(x\) be the number of liters of the 7% solution, then you will need \(5-x\) liters of the 12% solution.

The first solution will have \(0.07x\) total liters of the solution, and the second would have \(0.12(5-x)\). Pooling them together gives you
\[0.07x+0.12(5-x)\]
and you want this to make a 5 liter mixture at 10% concentration, i.e. a mixture containing \(0.10\times5=0.5\) total liters of solution. This means you want to find the \(x\) that makes the equation true:
\[0.07x+0.12(5-x)=0.5\]