Solving a Value Mixture Problem Calculator

FAQs

How do you calculate mixture problems?

Mixture problems involve combining two or more substances with different concentrations to create a mixture of a desired concentration. The key steps to solving mixture problems are:

1. Identify the components and their concentrations in the initial solutions.
2. Determine the volume or quantity of each initial solution used (if not given, assume it).
3. Set up equations based on the amount of each component and the final desired concentration.
4. Solve the equations to find the unknown quantities.

Now, let’s address your specific mixture problems:

1. How many liters of each of a 12% and a 33% alcohol solution should be mixed to obtain 21 liters of a 25% solution?

Let x be the volume of the 12% solution and y be the volume of the 33% solution. We can set up two equations:

• Equation 1: x + y = 21 (total volume is 21 liters)
• Equation 2: (0.12x + 0.33y) / 21 = 0.25 (final concentration is 25%)

Solve this system of equations to find x and y.

2. How much of a 20% acid solution would a chemist have to mix with one liter of a 40% acid solution to yield a 36% acid solution?

Let x be the volume of the 20% solution needed. We can set up an equation:

• (0.20x + 0.40 * 1) / (x + 1) = 0.36 (final concentration is 36%)

Solve for x.

3. How many Liters of 20% alcohol solution should be added to 40 Liters of a 50% alcohol solution to make a 30% solution?

Let x be the volume of the 20% solution added. We can set up an equation:

• (0.20x + 0.50 * 40) / (x + 40) = 0.30 (final concentration is 30%)

Solve for x.

4. How many Liters of 3% alcohol solution should be mixed with 6 Liters of 30% alcohol solution to get a 12% solution?

Let x be the volume of the 3% solution needed. We can set up an equation:

• (0.03x + 0.30 * 6) / (x + 6) = 0.12 (final concentration is 12%)

Solve for x.

5. How many Liters of pure alcohol are there in 8 Liters of a 20% solution?

Multiply 8 liters by 0.20 (20%) to find the amount of pure alcohol.

6. How much 10% solution and how much 45% solution should be mixed together to make 100 gallons of 25% solution?

Let x be the volume of the 10% solution and y be the volume of the 45% solution. We can set up two equations:

• Equation 1: x + y = 100 (total volume is 100 gallons)
• Equation 2: (0.10x + 0.45y) / 100 = 0.25 (final concentration is 25%)

Solve this system of equations to find x and y.

7. How many liters of a 10% acid solution must be mixed with 10 liters of a 4% solution to obtain a 6% solution?

Let x be the volume of the 10% solution needed. We can set up an equation:

• (0.10x + 0.04 * 10) / (x + 10) = 0.06 (final concentration is 6%)

Solve for x.

8. What amount of a 60% acid solution must be mixed with a 30% solution to produce 300 ml of a 50% solution?

Let x be the volume of the 60% solution needed. We can set up an equation:

• (0.60x + 0.30(300 – x)) / 300 = 0.50 (final concentration is 50%)

Solve for x.

9. How many gallons of a 5% acid solution must be mixed with 5 gallons of 10% solution to obtain a 7% solution?

Let x be the volume of the 5% solution needed. We can set up an equation:

• (0.05x + 0.10 * 5) / (x + 5) = 0.07 (final concentration is 7%)

Solve for x.

10. How much 20% alcohol is required to make 1 liter of 10% alcohol?

Let x be the amount of 20% alcohol needed. We can set up an equation:

• (0.20x) / 1 = 0.10 (final concentration is 10%)

Solve for x.

If you have more specific questions or need further assistance with any of these problems, please let me know.