A nurse mixes 60 cc of a 50% saline solution with a 10% saline solution to produce a 25% saline solution. How much of the 10% solution should he use?

To solve this problem, let's define the amount of the 10% saline solution to be used as \( x \) cc.

We know the following:
- The nurse mixes 60 cc of a 50% saline solution.
- The goal is to produce a 25% saline solution by mixing it with a certain amount of 10% saline solution.
- The final concentration should be 25%, and the total volume will be \( 60 + x \) cc.

### Step 1: Calculate the amount of salt in each solution.
- The amount of salt in 60 cc of the 50% saline solution is \( 0.5 \times 60 = 30 \) cc of salt.
- The amount of salt in \( x \) cc of the 10% saline solution is \( 0.1 \times x = 0.1x \) cc of salt.
- The amount of salt in the final 25% saline solution (with a total volume of \( 60 + x \) cc) is \( 0.25 \times (60 + x) = 0.25(60 + x) \) cc of salt.

### Step 2: Set up the equation.
The amount of salt in the mixture before and after mixing must be the same. Therefore, we can write the equation:
\[
30 + 0.1x = 0.25(60 + x)
\]

### Step 3: Solve the equation.
Expand the equation on the right side:
\[
30 + 0.1x = 15 + 0.25x
\]
Now, move all terms involving \( x \) to one side and the constants to the other:
\[
30 - 15 = 0.25x - 0.1x
\]
Simplify:
\[
15 = 0.15x
\]
Solve for \( x \):
\[
x = \frac{15}{0.15} = 100
\]

### Answer:
The nurse should use **100 cc** of the 10% saline solution.

Would you like further details or have any questions?

Here are 5 related questions you might find helpful:
1. How do you calculate the concentration of a solution?
2. What other methods can be used to mix solutions with different concentrations?
3. How do ratios apply to problems involving mixtures?
4. Can this method be used for other types of mixtures, such as medicines?
5. What is the importance of understanding solution concentrations in healthcare?

**Tip:** When solving mixture problems, always make sure the amount of the substance being mixed (like salt here) is conserved throughout the process.

Learn how to solve a mixture problem where 60 cc of a 50% saline solution is mixed with a 10% saline solution to produce a 25% solution. This step-by-step guide covers key algebraic concepts and shows how to set up and solve linear equations. Suitable for students in Grades 8-10.

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