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%

Let's denote the number of panels produced by Plant B as $ x $.

Given:
- Plant A produced 3000 panels.
- 3% of Plant A's panels were defective.
- 10% of Plant B's panels were defective.
- The overall percentage of defective panels was 7%.

We can set up the equation based on the total number of defective panels:

### Step 1: Calculate the number of defective panels from each plant.
- Defective panels from Plant A: $ 0.03 \times 3000 = 90 $
- Defective panels from Plant B: $ 0.10 \times x = 0.10x $

### Step 2: Set up the equation for the overall percentage of defective panels.
The total number of panels produced by both plants is $ 3000 + x $.

The total number of defective panels from both plants is $ 90 + 0.10x $.

The overall percentage of defective panels is given as 7%, so:

\[
\frac{90 + 0.10x}{3000 + x} = 0.07
\]

### Step 3: Solve the equation.
Multiply both sides by $ 3000 + x $ to get rid of the fraction:

\[
90 + 0.10x = 0.07(3000 + x)
\]

Expand and simplify:

\[
90 + 0.10x = 210 + 0.07x
\]

Subtract $ 0.07x $ from both sides:

\[
90 + 0.03x = 210
\]

Subtract 90 from both sides:

\[
0.03x = 120
\]

Divide both sides by 0.03:

\[
x = \frac{120}{0.03} = 4000
\]

So, Plant B produced 4000 panels.

Would you like further details or have any questions?

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Here are five related questions you might explore:
1. What would be the new overall defective percentage if Plant B produced 5000 panels instead of 4000?
2. How would the overall defective rate change if Plant A produced 500 more panels, all of which were non-defective?
3. What if Plant A increased its production to 4000 panels, maintaining the same defective percentage?
4. How many defective panels would there be if both plants had an equal defective rate of 5%?
5. How does the defective rate impact the overall production cost if each defective panel results in a $50 loss?

**Tip:** When dealing with percentage problems, setting up a clear equation helps simplify the process of finding the unknown.

Learn how to calculate the number of panels produced by Plant B in a scenario involving defective rates. Solve the problem step-by-step with detailed equations and calculations. Discover related questions and explore variations in production and defective rates.

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