3 ounces of a 16% alcohol solution must be mixed with 3 ounces of a 20% alcohol solution to make a 18% alcohol solution.
To determine the quantity of a 16% alcohol solution required to mix with 3 ounces of a 20% alcohol solution to obtain an 18% alcohol solution, we can use a simple algebraic equation. Let's represent the unknown amount of the 16% solution as "x" (in ounces).
The equation can be set up as follows:
0.16x + 0.20(3) = 0.18(x + 3)
Simplifying the equation:
0.16x + 0.6 = 0.18x + 0.54
Rearranging and combining like terms:
0.16x - 0.18x = 0.54 - 0.6
Simplifying further:
-0.02x = -0.06
Dividing both sides by -0.02:
x = (-0.06) / (-0.02) = 3
Therefore, to achieve an 18% alcohol solution, you would need to mix 3 ounces of the 16% alcohol solution with the 3 ounces of the 20% alcohol solution.