# What masses of salt solutions with mass fractions of 5% and 25% should be taken to prepare

What masses of salt solutions with mass fractions of 5% and 25% should be taken to prepare a solution of this salt with a mass fraction of 20% and a mass of 150 grams.

Given:
ω1 (salt) = 5%
ω2 (salt) = 25%
ω3 (salt) = 20%
m3 solution (salt) = 150 g

Find:
m1 solution (salt) -?
m2 solution (salt) -?

1) Let m1 solution (salt) = (x) z, and m2 solution (salt) = (y) z;
2) m1 (salt) = ω1 * m1 solution / 100% = 5% * x / 100% = (0.05x) g;
3) m2 (salt) = ω2 * m2 solution / 100% = 25% * y / 100% = (0.25y) g;
4) m3 (salt) = ω3 * m3 solution / 100% = 20% * 150/100% = 30 g;
5) m3 (salt) = m1 + m2 = (0.05x + 0.25y) g;
6) m3 solution (salt) = m1 solution + m2 solution = (x + y) g;
7) 0.05x + 0.25y = 30;
x + y = 150;
y = 150 – x;
0.05x + 0.25 * (150 – x) = 30;
x = 37.5;
8) m1 solution (salt) = x = 37.5 g;
9) m2 solution (salt) = y = 150 – x = 150 – 37.5 = 112.5 g.

Answer: The weights of the solutions are 37.5 g and 112.5 g, respectively.

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