Two factory plants are making TV panels. Yesterday, Plant A produced
20,000
panels. Ten percent of the panels from Plant A and
3%
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
8%
?
Let's assume the number of panels produced by Plant B is x.
Step 1: Calculate the number of defective panels produced by Plant A
Defective panels from Plant A = 10% of 20,000 = (10/100) * 20,000 = 2,000
Step 2: Calculate the number of defective panels produced by Plant B
Defective panels from Plant B = 3% of x = (3/100) * x = 0.03x
Step 3: Calculate the overall number of defective panels
Total defective panels = Defective panels from Plant A + Defective panels from Plant B
8% of total panels = (8/100) * (20,000 + x)
Total defective panels = (8/100) * (20,000 + x)
Step 4: Set up an equation
Total defective panels = Defective panels from Plant A + Defective panels from Plant B
(8/100) * (20,000 + x) = 2,000 + 0.03x
Step 5: Solve the equation
(8/100)*(20,000 + x) = 2000 + 0.03x
(8/100)*(20,000) + (8/100)*x = 2000 + 0.03x
1600 + 0.08x = 2000 + 0.03x
0.08x - 0.03x = 2000 - 1600
0.05x = 400
x = 400/0.05
x = 8,000
Therefore, Plant B produced 8,000 panels.
To find out how many panels Plant B produced, we need to use the given information and some algebraic manipulation. Let's break down the problem step by step:
1. We know that Plant A produced 20,000 panels yesterday.
2. The percentage of defective panels from Plant A is 10%, which means 10% of the panels from Plant A were defective. To calculate this, we multiply the number of panels from Plant A (20,000) by 10% (0.10):
Defective panels from Plant A = 20,000 x 0.10 = 2,000 panels
3. We also know that the overall percentage of defective panels from the two plants is 8%.
4. Let's assume Plant B produced "x" panels. The percentage of defective panels from Plant B is 3%, which means 3% of the panels from Plant B were defective. To calculate this, we multiply the number of panels from Plant B ("x") by 3% (0.03):
Defective panels from Plant B = x x 0.03 = 0.03x panels
5. The total number of defective panels is the sum of defective panels from Plant A and Plant B, and it should be 8% of the total number of panels produced:
Total defective panels = Defective panels from Plant A + Defective panels from Plant B
8% of the total panels = (Defective panels from Plant A + Defective panels from Plant B) = 0.08 x (20,000 + x)
6. Now we can set up an equation based on the previous step:
8% of the total panels = Defective panels from Plant A + Defective panels from Plant B
0.08 x (20,000 + x) = 2,000 + 0.03x
7. Solve the equation for "x":
0.08x + 1600 = 2000 + 0.03x
0.05x = 400
x = 400 / 0.05
x = 8000
Therefore, Plant B produced 8,000 panels.