Question

How many liters of 15% acid and 33% acid should be mixed to make 40 liters of 21% acid solution?

a) X and X

b) Y and Y

Answer 1

To find the necessary volumes of 15% and 33% acid required to create 40 liters of a 21% acid solution, construct a system of algebraic equations based on total volume and concentration, and solve using substitution or elimination.

Without the specific numerical values for X and Y, the correct answer format cannot be determined. It should be numerical values, not X and X or Y and Y. If you provide the specific values or if the answer choices are in numerical form, I can assist further.

Step-by-step explanation:

Let's denote the volume of the 15% acid solution as X and the volume of the 33% acid solution as Y.

The total volume of the mixture is given as 40 liters.

So, we have the equation:

`\[ X + Y = 40 \]`

Now, let's express the amount of acid in each solution:

For the 15% acid solution:

Acid content = 0.15X (15% of X)

For the 33% acid solution:

Acid content = 0.33Y (33% of Y)

The total amount of acid in the mixture is given as 21% of the total volume:

`\[ 0.21 * 40 \, \text{liters} = 0.15X + 0.33Y \]`

Simplify the equation:

`\[ 8.4 = 0.15X + 0.33Y \]`

Now, we have a system of two equations:

`\[ \begin{cases} X + Y = 40 \\ 0.15X + 0.33Y = 8.4 \end{cases} \]`

You can solve this system to find the values of X and Y. The solution will provide the volumes of the 15% and 33% acid solutions needed to make 40 liters of a 21% acid solution.

Without the specific numerical values for X and Y, the correct answer format cannot be determined. It should be numerical values, not X and X or Y and Y. If you provide the specific values or if the answer choices are in numerical form, I can assist further.