Question

Two factory plants are making TV panels. Yesterday, Plant A produced 4000 panels. One percent of the panels from Plant A and 4% 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 2% ?

Answer 1

By setting up an equation to calculate the number of panels that Plant B produced, given the defect rates of Plant A, Plant B, and the combined defect rate of both plants, we find that Plant B produced 2000 panels.

Step-by-step explanation:

To solve the question of how many TV panels Plant B produced, given that Plant A produced 4000 panels with a defect rate of 1%, and that the overall defect rate from both plants is 2%, we can set up an equation.

Let x represent the number of panels Plant B produced. Plant B has a 4% defect rate. The total number of defective panels from Plant A is 1% of 4000, which is 40 panels. The number of defective panels from Plant B is 4% of x.

Since the overall defect rate is 2%, the combined defective panels from both plants (which is 40 + 0.04x) would be 2% of the total production (which is 4000 + x).

Thus, we have the equation:

40 + 0.04x = 0.02(4000 + x)

By solving this equation, we find that:

40 + 0.04x = 80 + 0.02x

0.04x - 0.02x = 80 - 40

0.02x = 40

x = 40 / 0.02

x = 2000

Therefore, Plant B produced 2000 TV panels.