Question

Two factory plants are making tv panels. Yesterday, plant A produced 2000 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 5%?

Answer 1

Let B be the amount of panels that plant B produced.

The total amount of defective panels from plant A is:

`(10)/(100)*2000=200`

The total amount of defective panels from plant B is:

`(3)/(100)* B=0.03B`

The total amount of panels produced by plants A and B is:

`2000+B`

Since 5% of the total of panels is defective, the total amount of defective panels is:

`\begin{gathered} (5)/(100)*(2000+B) \\ =100+0.05B \end{gathered}`

On the other hand, the total amount of defective panels is the sum of the defective panels from plants A and B:

`200+0.03B`

Since these two expressions correspond to the total amount of defective panels, then:

`200+0.03B=100+0.05B`

Solve for B:

`\begin{gathered} \Rightarrow200-100=0.05B-0.03B \\ \Rightarrow100=0.02B \\ \Rightarrow B=(100)/(0.02) \\ \Rightarrow B=5000 \end{gathered}`

Therefore, the total amount of panels that plant B produced, is:

`5000`