Let's solve the equation:

\[
0.18X + 0.13(1 - X) = 0.16
\]

### Step 1: Distribute the \(0.13\) on the right-hand side.
\[
0.18X + 0.13 - 0.13X = 0.16
\]

### Step 2: Combine like terms on the left-hand side.
\[
(0.18X - 0.13X) + 0.13 = 0.16
\]
\[
0.05X + 0.13 = 0.16
\]

### Step 3: Subtract 0.13 from both sides to isolate the term with \(X\).
\[
0.05X = 0.16 - 0.13
\]
\[
0.05X = 0.03
\]

### Step 4: Divide both sides by 0.05 to solve for \(X\).
\[
X = \frac{0.03}{0.05}
\]
\[
X = 0.6
\]

So, the solution is \( X = 0.6 \).

Would you like more details or have any questions?

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Here are some related questions:
1. How would the equation change if the percentages were different?
2. What does the solution \(X = 0.6\) represent in a real-world context?
3. How would you solve this equation if it were set up with decimals instead of percentages?
4. Can you create a similar equation with a different solution?
5. What would happen to the solution if both sides of the equation were multiplied by 100?

**Tip:** When dealing with percentages in equations, remember that 18% can be written as 0.18 for easier calculations.

Learn how to solve the linear equation involving percentages: 18%*X + 13%(1-X) = 16%. This problem covers percentage calculations and algebraic manipulation. Suitable for students in Grades 7-9.

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