To solve the equation \( D \times 0.97 + (10,000 - D) \times 0.02 = 4,000 \), follow these steps:

1. Distribute the terms inside the parentheses:
   \[
   D \times 0.97 + 10,000 \times 0.02 - D \times 0.02 = 4,000
   \]

2. Simplify the constants:
   \[
   0.97D + 200 - 0.02D = 4,000
   \]

3. Combine like terms:
   \[
   (0.97 - 0.02)D + 200 = 4,000
   \]
   \[
   0.95D + 200 = 4,000
   \]

4. Subtract 200 from both sides:
   \[
   0.95D = 3,800
   \]

5. Divide both sides by 0.95:
   \[
   D = \frac{3,800}{0.95}
   \]
   \[
   D = 4,000
   \]

So, the value of \( D \) is \( 4,000 \).

Would you like more details or have any questions?

Here are some related questions you might find interesting:

1. How do you solve linear equations with one variable?
2. What are some common techniques for solving equations with multiple variables?
3. Can you explain the concept of distributing terms in algebra?
4. How do you combine like terms in an equation?
5. What is the significance of isolating the variable in an equation?
6. How do you handle equations with parentheses and multiple operations?
7. What are the steps to check if a solution to an equation is correct?
8. Can you show examples of solving real-life problems using linear equations?

**Tip:** Always double-check your solution by plugging it back into the original equation to ensure it satisfies all parts of the equation.

Learn how to solve the equation D×0.97+(10,000−D)×0.02=4,000 with a detailed step-by-step solution. This problem involves linear equations and the distributive property, suitable for students in Grades 7-9.

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