Raul has one solution that is 20% acid by volume and one solution that is 50% acid by volume. he plans to mix together some of each solution to create 30 milliliters of a solution that is 40% acid by volume. how many milliliters of the 20% acid solution should raul use to create the 40% acid solution? can someone explain this to me? i know that the answer is 10 milliliters, but i don't know how to get it.

20 ml of the substance with 50% of acid and 10ml of the substance with 20% of acid.

Explanation:

Let's define X as the ml of the substance that is 20% acid and Y as the substance that has 50% of acid.

We want to craft a substance that of 30 ml that has a 40% of acid.

where, for example, 20% of the acid in the X ml is 0.2*X ml of acid.

The equations that we have is:

a) X + Y = 30

b) X*0.2 + Y*0.5 = 0.4*30

The first step is isolate one of the variables in one of the equations, lets isolate X in a.

X = 30 - Y

now we can replace it in the equation b, and solve the equation for Y.

X*0.2 + Y*0.5 = 0.4*30

(30 - Y)*0.2 + Y*0.5 = 0.4*30

6 - Y*0.2 + Y*0.5 = 12

Y*(0.5 - 0.2) = 6

Y*0.3 = 6

Y = 6/0.3 = 20

So we must use 20 ml of the substance with 50% of acid, and the other 10 ml must be the substance of 20% of acid.