Problem

You poured some 12% alcohol solution and some 6% alcohol solution into a mixing container. Now you have 480 grams of 8% alcohol solution. How many grams of 12% solution and how many grams of 6% solution did you pour into the mixing container?

Write and solve a system equation to answer the following questions.
You mixed grams of 12% solution with grams of 6% solution.

Answer

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Answer

So, the final answer is: You mixed 160 grams of 12% solution with 320 grams of 6% solution.

Steps

Step 1 :Let's denote the amount of 12% solution as x and the amount of 6% solution as y.

Step 2 :From the problem, we know that the total amount of solution is 480 grams, so we have the equation x+y=480.

Step 3 :We also know that the final solution is 8% alcohol, so the total amount of alcohol from the 12% solution and the 6% solution should be 8% of the total solution. This gives us the equation 0.12x+0.06y=0.08×480.

Step 4 :We can solve the first equation for x, which gives us x=480y.

Step 5 :Substitute x=480y into the second equation, we get 0.12(480y)+0.06y=38.4.

Step 6 :Solving this equation for y, we get y=320.

Step 7 :Substitute y=320 back into the first equation, we get x=480320=160.

Step 8 :So, the final answer is: You mixed 160 grams of 12% solution with 320 grams of 6% solution.

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