Question

Determine the number of liters of a 30% saline solution and the number of liters of a 60% saline solution that are required to make 10 liters of a 50% saline solution.

Answer 1

Using a system of equations, we find that 2 liters of a 30% saline solution and 8 liters of a 60% saline solution are needed to make 10 liters of a 50% saline solution.

Step-by-step explanation:

To determine the number of liters of a 30% saline solution and the number of liters of a 60% saline solution required to make 10 liters of a 50% saline solution, we can set up a system of equations based on the principle of conservation of mass.

Steps to solve the problem:

1. Let x represent the volume in liters of the 30% solution, and y represent the volume in liters of the 60% solution.
2. The total volume should be 10 liters: x + y = 10.
3. The total amount of saline in the final solution should be 50% of 10 liters: 0.30x + 0.60y = 0.50 × 10.
4. Now we have two equations: x + y = 10 and 0.30x + 0.60y = 5.
5. Multiply the first equation by 0.30 to facilitate elimination: 0.30x + 0.30y = 3.
6. Subtract this new equation from the second equation to find the value of y.
7. Substitute the value of y back into x + y = 10 to solve for x.

Solving these equations, we obtain x = 2 liters of the 30% solution and y = 8 liters of the 60% solution.

Answer 2

Number of liters of 30% solution = x = 3.3 liters

Number of liters of 60% solution = y

= 6.67 liters

Step-by-step explanation:

Let us represent:

Number of liters of 30% solution = x

Number of liters of 60% solution = y

Determine the number of liters of a 30% saline solution and the number of liters of a 60% saline solution that are required to make 10 liters of a 50% saline solution.

30% × x + 60% × y = 10 × 50%

0.3x + 0.6y = 5...... Equation 1

x + y = 10...... Equation 2

x = 10 - y

We substitute 10 - y for x in Equation 1

Hence

0.3(10 - y) + 0.6y = 5

3 - 0.3y + 0.6y = 5

- 0.3y + 0.6y = 5 - 3

0.3y = 2

y = 2/0.3

y = 6.67 liters

Solving for x

x = 10 - y

x = 10 - 6.67

x = 3.33 liters

Hence:

Number of liters of 30% solution = x = 3.3 liters

Number of liters of 60% solution = y

= 6.67 liters