Final answer:
To make a 16% alcohol solution, 8 ounces of a 13% alcohol solution must be mixed with 6 ounces of a 20% alcohol solution.
Step-by-step explanation:
To determine how many ounces of a 13% alcohol solution must be mixed with 6 ounces of a 20% alcohol solution to make a 16% alcohol solution, we can set up an equation using the concept of a weighted average. Let x represent the number of ounces of the 13% solution we need. Then the total amount of alcohol from both solutions, when mixed, should equal the total amount of alcohol in the final 16% solution.
The equation representing this situation is:
- 0.13x (from the 13% solution) + 0.20×6 (from the 20% solution) = 0.16(x + 6) (from the final 16% solution)
We simplify this equation:
- 0.13x + 1.2 = 0.16x + 0.96
- Subtract 0.13x from both sides: 1.2 = 0.03x + 0.96
- Subtract 0.96 from both sides: 0.24 = 0.03x
- Divide both sides by 0.03: x = 8 ounces
Therefore, 8 ounces of a 13% alcohol solution must be mixed with 6 ounces of a 20% alcohol solution to obtain a 16% alcohol solution.