Question

How many liters of water must Sharon add to 2 liters of a sugar and water solution that is 36% sugar to create a solution that is 12% sugar?

Answer 1

The amount of sugar $x$ in the starting solution contributes to a 36% concentration, so we have

$\dfrac x2=0.36\implies x=0.64$

units of sugar in the solution.

Into this solution, Sharon wants to pour $y$ liters of water to obtain a smaller concentration of sugar in the overall solution:

$\dfrac{0.64}{2+y}=0.12\implies\dfrac{16}3=2+y\implies y=\dfrac{10}3\approx3.33$

So Sharon needs to add $\dfrac{10}3$ liters of water to the solution to get the desired concentration.