Calculate how much water you need to add to 45 g of sugar to get a 10% solution.

When solving such problems, the formula is applied:
W% = [m (w-va). 100%] / m (p-pa), where
W% – mass fraction of the solution; m (in-va) is the mass of the dissolved substance; m (p-pa) is the mass of the solution.
From the formula we calculate the mass of the solution, we get:
m (p-pa) = [m (in-va). 100%] / w% = (45 g. 100%) / 10% = 450 g.
The mass of the solution is the mass of water) and the mass of the dissolved substance:
m (p-pa) = m (in-va) + m (H2O).
From here we calculate how much water should be added to 45 g of sugar, we get:
m (H2O) = m (p-pa) – m (v-va) = 450 – 45 = 405 g.
Answer: m (H2O) = 405 g.

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