How many grams of sodium chloride should be dissolved in 500 g of a 1.5% solution of the same salt to obtain a 5.2% solution?

Let’s write down given:
m (NaCl solution) = 500 g
w (NaCl) = 1.5% or 0.015
w (1) (NaCl) = 5.2% or 0.052
Calculate m (NaCl) to be added to the solution -?

Decision :
The mass fraction of the solute is equal to: the ratio of the mass of the solute to the mass of the solution and multiplied by 100% (if converted to percentages).
w = m (substance) / a, here m (substance) = w * m (solution)
Let’s find the mass of the substance in this solution:
m (NaCl) = 500 g * 0.015 = 7.5 g
When a substance is added to a solution, the mass of the solute and the mass of the solution increase. Let the mass of the added substance be x g. Then m (NaCl) = 7.5 g + x g, and m (solution) = 500 g + 7.5. Let’s calculate the m-value of x.
0.052 = (7.5 + x) / (500 + x)
0.052 * (500 + x) = (7.5 + x)
Solving the equation: 26 + 0.052 x = 7.5 + x
18.5 = 0.948 x
x = 18.5 / 0.948
x = 19.51 g (NaCl)
Answer: It is necessary to add 19.51 g of sodium chloride to the solution.