100 g of water was added to the aqueous salt solution. As a result, the salt concentration in the solution

100 g of water was added to the aqueous salt solution. As a result, the salt concentration in the solution decreased by 1%. Determine the initial mass of the solution if it is known that it contained 30 g of salt.

Let X gram be the mass of the entire solution.
The concentration of the solution is found by the formula:
W = (Mass of substance) / mass of solution * 100%.
Salt is a substance. For two solutions, its weight is the same – 30 grams.
The mass of water in the second solution was 100 grams more, which means that the mass of the solution itself was 100 grams more, therefore, the mass of the second solution was 100 + X grams.
Let’s compose and solve the equation:
30 / X * 100 – 30 / (100 + X) * 100 = 1;
3000 / X – 3000 / (100 + X) = 1;
3000 * (100 + X) – 3000 * X = 1 * X * (100 + X;
300000 + 3000X – 3000X = 100X + X ^ 2;
300,000 – 100X – X ^ 2 = 0;
-X ^ 2 – 100X + 300000 = 0;
X ^ 2 + 100X – 300000 = 0;
D1 = (100/2) ^ 2 – (-300000) = 50 ^ 2 + 300000 = 2500 + 300000 = 302500.
√D1 = √302500 = 550.
X1 = (-100/2) – 550 = -50 – 550 = -600 – does not satisfy the condition of the problem.
X2 = (-100/2) + 550 = -50 + 550 = 500.
Thus, the initial mass of the solution is 500 grams.
Answer: 500 grams.