How many kilograms of pure alcohol must be added to 40 kg of a 70% alcohol solution to produce an 85% alcohol solution?
To solve this problem, we need to use the concept of mixing solutions. Here's how you can find the answer:
Step 1: Understand the problem.
We have a 70% alcohol solution which weighs 40 kg. We need to add some amount of pure alcohol (100% alcohol) to this solution to make an 85% alcohol solution. The question is asking for the quantity of pure alcohol needed.
Step 2: Set up the equation.
Let's assume we need to add x kg of pure alcohol. The equation can be set up as follows:
40 kg of 70% alcohol solution + x kg of 100% alcohol = (40 + x) kg of 85% alcohol solution.
Step 3: Calculate the amount of alcohol in each component.
The amount of alcohol in the 70% alcohol solution can be calculated by multiplying the weight of the solution by the alcohol concentration in decimal form. The amount of alcohol in x kg of pure alcohol is just x kg since it is 100% alcohol. So, we have:
0.7 * 40 + 1 * x = 0.85 * (40 + x).
Step 4: Solve the equation.
Now, we can solve the equation for x. Let's simplify it:
28 + x = 34 + 0.85x.
Combining like terms:
x - 0.85x = 34 - 28,
0.15x = 6.
Divide both sides of the equation by 0.15:
x = 6 / 0.15,
x = 40.
Therefore, 40 kg of pure alcohol must be added to the 40 kg of 70% alcohol solution to produce an 85% alcohol solution.