Final answer:
To prepare 300 mL of a 60% alcohol solution, mix 200 mL of 70% alcohol elixir with 100 mL of 40% alcohol elixir.
Step-by-step explanation:
To solve how many mL of 70% and 40% alcohol elixirs should be mixed to prepare 300 mL of 60% alcohol, we can use the concept of mixture problems in algebra. The equation for the mixture can be set up as follows:
Let x be the amount of 70% alcohol solution and 300-x be the amount of 40% alcohol solution. Then, the total amount of pure alcohol in the final mixture should be 60% of 300 mL.
70% of x + 40% of (300-x) = 60% of 300
0.70x + 0.40(300-x) = 0.60 × 300
0.70x + 120 - 0.40x = 180
0.30x = 60
x = 200 mL
Therefore, you need 200 mL of 70% alcohol and 100 mL of 40% alcohol to make 300 mL of a 60% alcohol solution.