Question

How many panels did Plant B produce, if the overall percentage of defective panels from the two plants was 8%?

Answer 1

`5000`

Step-by-step explanation

The number of panels produced by plant A is 2000.

Let the number of panels produced by plant B be b.

3% of panels from plant A and 10% of panels from plant B be were defective, and the total percentage of defective panels from both plants is 8%.

This implies that the sum of 3% of panels from plant A and 10% of panels from plant B is equal to 8% of the sum of panels from plants A and B.

That is:

`((3)/(100)\cdot2000)+((10)/(100)\cdot b)=((8)/(100))\cdot(2000+b)`

To find the number of panels produced by plant B, solve for b in the equation above:

`\begin{gathered} 60+0.1b=0.08(2000+b) \\ \Rightarrow60+0.1b=160+0.08b \\ 0.1b-0.08b=160-60 \\ 0.02b=100 \\ \Rightarrow b=(100)/(0.02) \\ b=5000 \end{gathered}`

That is the number of panels produced by plant B.