Answer: 7 liters of 6% alcohol solution.
Step-by-step explanation:
We have 7 liters of 10% alcohol solution, and in this the total amount of alcohol is
A = (10%/100%)*7 L = 0.1*7L = 0.7L
Now, suppose that we add N liters of 6% alcohol solution, then we have a total of:
(N + 7) Liters
And the total amount of alcohol would be:
(6%/100%)*N + 0.7L
0.06*N + 0.7L
The quotient between the total volume of alcohol and the total volume of liquid needs to be 0.08 (because we want a percentage of 8% of alcohol, and the decimal form of 8% is 0.08)
Then:
(0.06*N + 0.7L)/(N + 7L) = 0.08
We want to sove this for N
(0.06*N + 0.7L) = 0.08*(N + 7L)
0.06*N + 0.7L = 0.08*N + 0.56L
0.7L - 0.56L = 0.08*N - 0.06*N
0.14 L = 0.02*N
0.14L/0.02 = N = 7L
Then we need to add 7 liters of 6% alcohol solution.
