In this task, you need to determine the mass of a 30% solution if the following data are known:
Mass fraction of the first solution is 10%.
Mass fraction of the second solution is 30%.
The resulting solution is 15%.
The mass of the resulting solution is 300 g.
Write down the order of solving this problem.
Label the mass of the first solution through x.
Calculate the mass of the second solution.
Make up an expression.
Write down the solution to determine the mass of the 30% solution
Label the mass of the first solution through x. Determine the mass of the second solution if the total mass is known to be 300 g.
300 – x.
Consequently, the mass of the second solution is 300 – x.
Write an expression with an unknown x value.
0.1x + 0.3 (300 – x) = 0.15 * 300.
0.1x + 0.3 * 300 – 0.3x = 45.
0.1x + 90 – 0.3x = 45.
Next, it is necessary to transfer the known values in one direction, and the unknown values in the other direction.
0.1x – 0.3x = 45 – 90.
– 0.2x = – 45.
X = 45: 0.2 = 225 g.
Therefore, the mass of a 10 percent solution is 225 grams.
300 – 225 = 75 g.
The mass of a 30 percent solution is 75 g.
Answer: The mass of a 30 percent solution is 75 grams.
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