Question

you poured some 6% alcohol solution and some 12% alcohol solution into a mixing container. now you have 640 grams of 9% alcohol solution. how many grams of 6% solution and how many grams of 12% solution did you pour into the mixing container?

Answer 1

Let x be the amount of 6% alcohol solution in grams and y be the amount of 12% alcohol solution in grams.

We know that the final volume of the mixture is 640 grams and the concentration of alcohol in the mixture is 9%. This gives us the equation:

0.06x + 0.12y = 0.09(640)

Simplifying, we get:

0.06x + 0.12y = 57.6

We also know that the total amount of solution in the mixing container is x + y, which is equal to 640 grams. This gives us another equation:

x + y = 640

We can solve for x or y in terms of the other variable by rearranging this equation. Let's solve for x:

x = 640 - y

Substituting this into the first equation, we get:

0.06(640 - y) + 0.12y = 57.6

Expanding and simplifying, we get:

38.4 - 0.06y + 0.12y = 57.6

0.06y = 19.2

y = 320

So we poured 320 grams of 12% alcohol solution and 320 grams of 6% alcohol solution into the mixing container.