## Mixture Problem Solver

### Result

Amount of Final Mixture: liters

## 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:

- Identify the components and their concentrations in the initial solutions.
- Determine the volume or quantity of each initial solution used (if not given, assume it).
- Set up equations based on the amount of each component and the final desired concentration.
- 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.

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