150 g of water was added to a 15% acid solution, after which the acid concentration

150 g of water was added to a 15% acid solution, after which the acid concentration in the solution turned out to be 10%, find the mass of the acid in the solution.

Let us denote the mass of the acid in the solution through k, and the mass of water in the solution through v.

Since the concentration of the solution was 15%, the following relationship takes place:

100 * k / (k + v) = 15,

Simplifying this ratio, we get:

100k = 15k + 15v;

100k -15k = 15v;

85k = 15v;

v = 85k / 15;

v = 17k / 3.

Since after adding 150 g of water, the concentration of the resulting solution turned out to be 10%, we can draw up the following equation:

100 * k / (k + 17k / 3 + 150) = 10,

solving which, we get:

100 * k / (20k / 3 + 150) = 10;

100k = 10 * (20k / 3 + 150);

10k = 20k / 3 + 150;

10k – 20k / 3 = 150;

10k / 3 = 150;

k / 3 = 150/10;

k / 3 = 15;

k = 15 * 3 = 45 g.

Answer: 45 g.