How many liters of 20% alcohol solution should Maria mix with 50 liters of a 60% alcohol solution to obtain a 30% solution?
ok, in the 50 liters, you get 30 liters of alcohol content. In the final mixture, you want 30 percent, so
.30(V+50)=30+.2V
check that. solve for V, the volume of 20percent.
Perfect thx!!
To solve this problem step-by-step, we can use the concept of the amount of pure alcohol in each solution.
Step 1: Calculate the pure alcohol in the 60% solution.
We have 50 liters of a 60% alcohol solution, so the pure alcohol in this solution is (60/100) * 50 = 30 liters.
Step 2: Set up the equation for the total pure alcohol in the final solution.
Let's assume Maria mixes x liters of the 20% alcohol solution.
The pure alcohol in the 20% solution is (20/100) * x = 0.2x liters.
Hence, the total pure alcohol in the final solution is 30 liters (from the 60% solution) plus 0.2x liters (from the 20% solution).
Step 3: Set up the equation for the total volume of the final solution.
The total volume of the final solution is 50 liters (from the 60% solution) plus x liters (from the 20% solution), which is equal to 50 + x liters.
Step 4: Set up the equation for the desired concentration of the final solution.
We want the final solution to be a 30% alcohol solution, which means the pure alcohol should be 30% of the total volume. Therefore, the equation is:
(30/100) * (50 + x) = 30 + 0.2x.
Step 5: Solve the equation.
Let's simplify and solve the equation:
0.3 * (50 + x) = 30 + 0.2x
15 + 0.3x = 30 + 0.2x (distributing 0.3 over 50 + x)
0.3x - 0.2x = 30 - 15 (grouping like terms)
0.1x = 15
x = 150
Therefore, Maria should mix 150 liters of the 20% alcohol solution with 50 liters of the 60% alcohol solution to obtain a 30% alcohol solution.
To solve this problem, we can use the concept of mixing different solutions with varying concentrations of alcohol.
Let's denote the unknown quantity of 20% alcohol solution as "x" (in liters).
To find the amount of alcohol in the final mixture, we can consider the following equation:
(total amount of alcohol in 20% solution) + (total amount of alcohol in 60% solution) = (total amount of alcohol in the 30% solution)
The total amount of alcohol in a solution can be calculated as:
(amount of solution) * (concentration of alcohol)
Applying this to our problem, we can write the equation:
(x liters) * (20%) + (50 liters) * (60%) = (x + 50 liters) * (30%)
Now we can solve for x:
0.20x + 0.60 * 50 = 0.30 * (x + 50)
0.20x + 30 = 0.30x + 15
30 - 15 = 0.30x - 0.20x
15 = 0.10x
x = 15 / 0.10
x = 150 liters
Therefore, Maria should mix 150 liters of the 20% alcohol solution with 50 liters of the 60% alcohol solution to obtain a 30% solution.