A chemical plant needs 120 kilograms of 20% acid. But there were acids of 10% and 35% concentration

A chemical plant needs 120 kilograms of 20% acid. But there were acids of 10% and 35% concentration in the warehouse. How much acid from each of these concentrations should be blended to meet the plant’s need?

Let x be the required amount of kilograms of 10% acid, and y – 35% acid.

The plant needs to get 120 kg.
Let us write the equation for the masses of solutions:
1) x + y = 120.

Convert percentages to fractions:
10% – 0.1;
35% – 0.35;
20% – 0.2;

So, we mix x kg of 10% acid and y kg of 35% acid.
X kg of 10% contains 0.1 ∙ x pure acid.
In y kg 35% – 0.35 ∙ y.
We want to get a 20% solution. It should contain 0.2 pure acid and consist of x kg 10% and y kg 35%.

Let us write the equation for the masses of acids in solutions:
2) 0.1 ∙ x + 0.35 ∙ y = 0.2 ∙ (x + y).

We got a system of equations:
1) x + y = 120.
2) 0.1 ∙ x + 0.35 ∙ y = 0.2 ∙ (x + y).
⇑⇓
1) x + y = 120.
2) 0.15 ∙ y = 0.1 ∙ x.
⇑⇓
1) x + y = 120.
2) y / x = 2/3.
⇓
x = 72.
y = 48.

Answer: You need to mix 72 kg of 10% and 48 kg of 35% acid.