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The problem in the image asks for the number of ounces of a 16% alcohol solution that must be mixed with 7 ounces of a 20% alcohol solution to make an 18% alcohol solution.

Let's define the following:

- Let \( x \) be the number of ounces of the 16% alcohol solution.
- The amount of alcohol in the 16% solution is \( 0.16x \) ounces.
- The amount of alcohol in the 20% solution is \( 0.20 \times 7 = 1.4 \) ounces.
- The total mixture will have \( x + 7 \) ounces.
- The amount of alcohol in the final mixture should be 18% of the total volume, i.e., \( 0.18 \times (x + 7) \) ounces.

Now, set up the equation based on the total amount of alcohol:

\[
0.16x + 1.4 = 0.18(x + 7)
\]

We can solve this step by step.

1. Expand the right side:

\[
0.16x + 1.4 = 0.18x + 1.26
\]

2. Move the terms involving \( x \) to one side and constants to the other:

\[
0.16x - 0.18x = 1.26 - 1.4
\]

\[
-0.02x = -0.14
\]

3. Solve for \( x \):

\[
x = \frac{-0.14}{-0.02} = 7
\]

So, you need to mix **7 ounces** of the 16% alcohol solution.

Would you like any further explanation on this, or help with a related topic?

Here are 5 related questions you might be interested in:
1. What happens if you mix different percentages of alcohol solutions?
2. How do you create a mixture with a specific alcohol concentration?
3. How does the total volume of a solution affect the final concentration?
4. What are some common applications of these types of mixture problems?
5. How do you solve mixture problems with more than two solutions?

**Tip:** Always verify that the concentration is consistent by checking both the alcohol content and total volume.

How many ounces of a 16% alcohol solution must be mixed with 7 ounces of a 20% alcohol solution to make an 18% alcohol solution?

Learn how to solve a mixture problem where 16% and 20% alcohol solutions are combined to form an 18% solution. This step-by-step solution covers key concepts such as percentages and linear equations. Suitable for students in Grades 8-10.

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