Two factory plants are making TV panels. Yesterday, Plant A produced 3000 panels. Three percent of the panels from Plant A and 10% of the panels from Plant B were defective. How many panels did Plant B produce, if the overall percentage of defective panels from the two plants was 7%6?

Let's solve the problem step by step.

Let:
- \( x \) be the number of panels produced by Plant B.

### Step 1: Determine the number of defective panels from each plant
- Plant A produced 3000 panels, and 3% of them were defective. So, the number of defective panels from Plant A is:
  \[
  0.03 \times 3000 = 90 \text{ defective panels}
  \]
- Plant B produced \( x \) panels, and 10% of them were defective. So, the number of defective panels from Plant B is:
  \[
  0.10 \times x = 0.1x \text{ defective panels}
  \]

### Step 2: Express the total number of defective panels and total panels produced
The overall percentage of defective panels from both plants was 7%. The total number of panels produced by both plants is:
\[
3000 + x
\]
And the total number of defective panels is:
\[
90 + 0.1x
\]

### Step 3: Set up the equation for the overall percentage of defective panels
According to the problem, the overall percentage of defective panels is 7%, so:
\[
\frac{90 + 0.1x}{3000 + x} = 0.07
\]

### Step 4: Solve the equation
First, eliminate the fraction by multiplying both sides by \( 3000 + x \):
\[
90 + 0.1x = 0.07 \times (3000 + x)
\]
Distribute \( 0.07 \):
\[
90 + 0.1x = 210 + 0.07x
\]
Next, isolate the terms involving \( x \):
\[
0.1x - 0.07x = 210 - 90
\]
Simplify:
\[
0.03x = 120
\]
Finally, solve for \( x \):
\[
x = \frac{120}{0.03} = 4000
\]

### Step 5: Conclusion
Plant B produced 4000 panels.

Would you like more details or have any questions about the solution?

Here are five related questions you might find interesting:
1. What would be the overall percentage of defective panels if Plant B produced 5000 panels instead?
2. How many defective panels would there be if Plant A's defect rate increased to 5%?
3. What is the total number of panels produced by both plants combined?
4. How would the solution change if the defect rate at Plant A decreased to 2%?
5. If Plant B increased its production by 20%, how many more panels would it produce?

**Tip:** When working with percentages, it's often useful to express them as decimals to make calculations easier. For example, 7% becomes 0.07 in decimal form.

Learn how to calculate the number of TV panels produced by Plant B, given the defect percentages of both plants. Solve the problem step-by-step with detailed mathematical equations and percentages. Suitable for advanced high school students and beyond.

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