How much

8

%

saline solution should Kent mix with

60

cubic centimeters (cc) of a

16

%

saline solution to produce an

11

%

saline solution?

To solve this problem, we need to determine how much of an 8% saline solution Kent should mix with 60 cubic centimeters (cc) of a 16% saline solution to produce an 11% saline solution.

Let \( x \) represent the amount (in cubic centimeters) of the 8% saline solution that Kent needs to mix.

### Step 1: Set up the equation
The total amount of saline solution after mixing will be \( x + 60 \) cc. The total amount of salt in the final solution should equal the sum of the salt from the two original solutions.

- The amount of salt in the 8% solution is \( 0.08x \) grams.
- The amount of salt in the 16% solution is \( 0.16 \times 60 = 9.6 \) grams.
- The amount of salt in the final 11% solution is \( 0.11 \times (x + 60) \) grams.

### Step 2: Write the equation
\[
0.08x + 9.6 = 0.11(x + 60)
\]

### Step 3: Solve the equation
First, expand the right side of the equation:
\[
0.08x + 9.6 = 0.11x + 6.6
\]

Next, subtract \( 0.08x \) from both sides:
\[
9.6 = 0.03x + 6.6
\]

Then, subtract 6.6 from both sides:
\[
3 = 0.03x
\]

Finally, solve for \( x \) by dividing both sides by 0.03:
\[
x = \frac{3}{0.03} = 100 \, \text{cc}
\]

### Final Answer
Kent should mix **100 cubic centimeters (cc)** of the 8% saline solution with 60 cc of the 16% saline solution to produce an 11% saline solution.

Would you like more details on this calculation or have any other questions?

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Here are 5 related questions for further exploration:
1. What if Kent needed to produce a 9% saline solution instead? How much of the 8% solution would be needed?
2. How would the solution change if the original saline solutions were in different concentrations, say 10% and 20%?
3. What is the general formula for finding the amount of one solution needed to mix with another to achieve a desired concentration?
4. How would the problem change if the total volume of the final solution were specified?
5. What would happen if Kent mixed equal parts of the 8% and 16% saline solutions? What concentration would result?

**Tip:** When solving mixture problems, it's helpful to think in terms of the amount of solute (e.g., salt) rather than the concentration alone.

Learn how to solve a mixture problem involving saline solutions. Find out how much 8% saline solution should be mixed with 60 cc of 16% saline solution to produce an 11% saline solution. This problem covers mixture problems, percentages, and linear equations. Suitable for students in Grades 9-12.

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