During a science experiment, Nico created a 32%alcohol solution by mixing 8 fluid ounces of a 50% alcohol solution with a certain amount of an 8% alcohol solution. How many fluid ounces of the 32% alcohol solution did he create?
let the certain amount of 8% stuff be x oz
.5(8) + .08x = .32(8+x)
solve for x
To find out how many fluid ounces of the 32% alcohol solution Nico created, we can use a mixture equation:
Let x be the amount of the 8% alcohol solution (in fluid ounces) that Nico mixed with the 50% alcohol solution.
The total amount of the resulting mixture is the sum of the amounts of the two solutions used: 8 + x.
Converting the percentages to decimals, the amount of alcohol in the 8% solution is 0.08x fluid ounces, and the amount of alcohol in the 50% solution is 0.5(8) = 4 fluid ounces.
In the resulting 32% alcohol solution, the amount of alcohol is 0.32(8 + x) fluid ounces.
Setting up the equation, we have:
0.08x + 4 = 0.32(8 + x)
Now, let's solve for x:
0.08x + 4 = 2.56 + 0.32x
Subtract 0.08x and 2.56 from both sides:
0.08x - 0.08x + 4 - 2.56 = 2.56 - 2.56 + 0.32x - 0.08x
1.44 = 0.24x
Divide both sides by 0.24:
1.44 / 0.24 = (0.24x) / 0.24
6 = x
Therefore, Nico mixed 6 fluid ounces of the 8% alcohol solution with 8 fluid ounces of the 50% alcohol solution.
To find out how many fluid ounces of the 32% alcohol solution Nico created, we can substitute the value of x back into the equation:
Amount of 32% alcohol solution = 0.32(8 + x)
Amount of 32% alcohol solution = 0.32(8 + 6)
Amount of 32% alcohol solution = 0.32(14)
Amount of 32% alcohol solution = 4.48
Therefore, Nico created 4.48 fluid ounces of the 32% alcohol solution.