Question

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 please explain this to me? I know that the answer is 10 milliliters​, but I don't know how to get it.

Answer 1

Answer: 4 = 4 (our answers are correct)

Explanation:et's begin by assigning letters to represent our two unknowns:

x (liters of 25% solution)

y (liters of 50% solution)

Our system of equations will consist of two equations:

Equation #1 (total volume of solution)

Equation #2 (total concentration of acid)

Our total volume of solution is 10 liters, which can be expressed as the sum of our unknowns:

Equation #1: x + y = 10

Our total concentration of acid can be expressed as the sum of the individual acid concentrations to make up the concentration of the final solution:

Equation #2: (0.25)(x) + (0.50)(y) =

(0.40)(10)

We can use Equation #1 to express one unknown in terms of the other and then plug that expression into Equation #2 to solve for one of the unknowns:

x + y = 10

y = 10 - x

Now we'll plug our expression for y in terms of x into Equation #2 and solve for x:

0.25(x) + 0.50(10 - x) = 0.40(10)

0.25x + 5 - 0.50x = 4

-0.25x = 4 - 5

-0.25x = -1

x = (-1)/(-0.25)

x = 4 (liters of 25% solution)

Now we'll plug our value for x into Equation #1 and solve for y:

4 + y = 10

y = 10 - 4

y = 6 (liters of 50% solution)

Finally, we will verify the correctness of our answers by plugging these values into Equation #2 to see if the sum of the component acid concentrations equals the final solution concentration:

0.25(4) + (0.50)(6) = 0.40(10)

1 + 3 = 4

Answer 2

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

Step-by-step 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.