How many grams of 15% and 60% solutions in acid must be mixed to obtain 90 g of 40% acid solution?

Let’s denote the required mass of a fifteen percent solution through x15, and the required mass of six ten percent solution through x60.

Then we can compose the following equations:

x15 + x60 = 90;

(15/100) * x15 + (60/100) * x60 = (40/100) * 90.

We solve the resulting system of equations.

Substituting into the second equation the value x60 = 90 – x15 from the first equation, we get:

0.15 * x15 + 0.6 * (90 – x15) = 36;

0.15 * x15 + 54 – 0.6 * x15 = 36;

54 – 0.45 * x15 = 36;

0.45 * x15 = 54 – 36;

0.45 * x15 = 18;

x15 = 18 / 0.45 = 40 g.

Find x60:

x60 = 90 – x15 = 90 – 40 = 50 g.

Answer: you need to take 40 g of a 15% solution and 50 g of a 60% solution.