Alyssa is a chemist with Gemco Pharmaceutical Company. She needs to prepare 12 ounces of 9% hydrochloric acid solution. The only solution she currently has available are 4% and 12% hydrocholoric acid. How much should she use of each solution to obtain the needed solution.

Question

Alyssa is a chemist with Gemco Pharmaceutical Company. She needs to prepare 12 ounces of 9% hydrochloric acid solution. The only solution she currently has available are 4% and 12% hydrocholoric acid. How much should she use of each solution to obtain the needed solution.

Answer 1

1ounce= 30ml

12x30ml =360ml
360ml x 9% = 32.4ml
4%X + 12Y(360ml-X)= 32.4ml
0.04X + 43.2ml + 0.12X = 32.4ml
0.076X = 10.8ml
x= 142.ml 4%
y = 360-142.1ml
y= 218ml 12%

Answer 2

To determine how much of each solution Alyssa should use to obtain the required concentration, we can set up a system of equations based on the given information.

Let's assume Alyssa uses x ounces of the 4% hydrochloric acid solution and y ounces of the 12% hydrochloric acid solution.

From the problem statement, we know that the total amount of solution required is 12 ounces. Therefore, we have the equation:
x + y = 12 ----(1)

We also know that the desired concentration of the hydrochloric acid solution is 9%. To calculate the concentration, we need to consider the amount of hydrochloric acid in each solution.

For the 4% solution, the amount of hydrochloric acid is 4% of x ounces, which is 0.04x ounces.

For the 12% solution, the amount of hydrochloric acid is 12% of y ounces, which is 0.12y ounces.

To obtain the desired concentration of 9%, the total amount of hydrochloric acid in the mixture should be 9% of 12 ounces (which is 0.09 * 12 = 1.08 ounces).

So, we have the equation:
0.04x + 0.12y = 1.08 ----(2)

Now we have a system of two equations (equations 1 and 2) with two variables (x and y). We can solve this system to find the values of x and y.

One possible method is to solve these equations using substitution or elimination. However, I will solve it using the substitution method for simplicity.

From equation (1), we have y = 12 - x. Now we can substitute this value for y in equation (2):

0.04x + 0.12(12 - x) = 1.08

Simplifying the equation:

0.04x + 1.44 - 0.12x = 1.08

-0.08x + 1.44 = 1.08

-0.08x = 1.08 - 1.44

-0.08x = -0.36

x = -0.36 / -0.08

x = 4.5

Now, substitute the value of x back into equation (1) to find y:

4.5 + y = 12

y = 12 - 4.5

y = 7.5

Therefore, Alyssa should use 4.5 ounces of the 4% hydrochloric acid solution and 7.5 ounces of the 12% hydrochloric acid solution to obtain the required 12 ounce, 9% hydrochloric acid solution.