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

How Many Panels Did Plant B Produce If The Overall Percentage Of Defective Panels From The Two Plants Was 8 class=

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ANSWER

[tex]5000[/tex]

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:

[tex](\frac{3}{100}\cdot2000)+(\frac{10}{100}\cdot b)=(\frac{8}{100})\cdot(2000+b)[/tex]

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

[tex]\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=\frac{100}{0.02} \\ b=5000 \end{gathered}[/tex]

That is the number of panels produced by plant B.

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