To solve the equation \(0.06(a + 392) + 0.1a = 344\), follow these steps:

1. **Distribute the \(0.06\) across the terms inside the parentheses:**

   \[
   0.06a + 0.06 \times 392 + 0.1a = 344
   \]

2. **Calculate \(0.06 \times 392\):**

   \[
   0.06 \times 392 = 23.52
   \]

   So, the equation now becomes:

   \[
   0.06a + 23.52 + 0.1a = 344
   \]

3. **Combine the like terms \(0.06a\) and \(0.1a\):**

   \[
   (0.06a + 0.1a) + 23.52 = 344
   \]

   \[
   0.16a + 23.52 = 344
   \]

4. **Isolate the variable term \(0.16a\):**

   Subtract \(23.52\) from both sides:

   \[
   0.16a = 344 - 23.52
   \]

   \[
   0.16a = 320.48
   \]

5. **Solve for \(a\):**

   Divide both sides by \(0.16\):

   \[
   a = \frac{320.48}{0.16}
   \]

   \[
   a = 2003
   \]

So, the solution is \( a = 2003 \).

Would you like more details or have any questions?

Here are 5 related questions you could explore:

1. How do you solve equations with more complex distributions?
2. What happens if the equation includes a negative coefficient?
3. How can you solve similar equations with fractions?
4. What if the equation had additional terms on both sides?
5. How do you verify your solution to an equation?

**Tip:** Always double-check your work by substituting your solution back into the original equation to ensure it satisfies the equation.

Learn how to solve the linear equation 0.06(a + 392) + 0.1a = 344 with a step-by-step guide. This problem involves using the distributive property, combining like terms, and isolating variables. Suitable for students in Grades 8-10.

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