# Initially, the sugar content in the solution was 30%. After another 100 g of sugar was added to the solution

Initially, the sugar content in the solution was 30%. After another 100 g of sugar was added to the solution, its content was 50%. What is the mass of the first solution.

1. Let’s express the percentages in shares:

30% = 0.3,

50% = 0.5.

2. Let the initial mass of the solution be x g, then the initial proportion of sugar was (0.3 * x), and after adding 100 g of sugar, the proportion of sugar in the solution was (0.5 * x). Let’s make the equation:

0.3 * x + 100 = 0.5 * (x + 100),

100 = 0.5 * (x + 100) – 0.3 * x,

100 = 0.2 * x + 50,

50 = 0.2 * x

x = 50 / 0.2,

x = 50 / (2/10).

To divide a number by a fraction, you need to multiply the given number by the number that is the reciprocal of the fraction, i.e.

x = 50 * (10/2),

x = 50 * 5,

x = 250 (g).

Answer: the mass of the first solution is 250 g.

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