Question

Maria has added 2 liters of pure alcohol to 8 liters of a 48% alcohol solution. What is the alcohol concentration of the resulting solution?

Answer 1

Alcohol concentration of the resulting solution = 58.4%

Explanation:

Maria has added 2 liters of pure alcohol to 8 liters of a 48% alcohol solution.

Volume of alcohol in 8 liters of a 48% alcohol solution is given by

`V_1=(48)/(100)* 8=3.84L`

New volume of alcohol added by maria, V₂ = 2 L

Total volume of solution, V = 8 + 2 = 10 L

Total volume of alcohol in 10 L solution, Vₐ = V₁ + V₂ = 3.84 + 2 = 5.84 L

`\texttt{Alcohol concentration of the resulting solution =}\frac{\texttt{Total volume of alcohol in 10 L solution}}{\texttt{Total volume of solution}}* 100\\\\\texttt{Alcohol concentration of the resulting solution =}(5.84)/(10)* 100\\\\\texttt{Alcohol concentration of the resulting solution =}58.4\%`

Alcohol concentration of the resulting solution = 58.4%

Answer 2

The alcohol concentration of the resulting solution is 58.4%

Explanation:

- At first we must to find the quantity of pure alcohol in the 8 liters

∵ The alcohol concentration is 48% in 8 liters

∴ The quantity of pure alcoholic =
`(48)/(100)*8=3.84` liters

- She added 2 liters pure alcohol to the solution that means the solution

increased by 2 liters and alcohol quantity increased by 2 liters

∵ She added 2 liters pure alcohol

∴ The quantity of pure alcohol = 2 + 3.84 = 5.84 liters

∴ The resulting solution = 2 + 8 = 10 liters

- Now we need to find the concentration of alcohol in the resulting

solution

∵ The quantity of pure alcohol = 5.84 liters

∵ The resulting solution = 10 liters

∴ The concentrate of alcohol =
`(5.84)/(10)*100` % = 58.4%

The alcohol concentration of the resulting solution is 58.4%