Question

Two factory plants are making TV panels. Yesterday, Plant A produced 24,000 panels. Six percent of the panels from Plant A and 2% 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

8000 panels

Explanation:

• Let the number of panels produced by plant B = b

,

• Percentage of defective panels from plant B = 2%

• The number of panels produced by plant A = 24,000

,

• Percentage of defective panels from plant A = 6%

Combining from Plant A and Plant B:

• The total number of panels = 24,000+b

,

• The percentage of defective panels from the two plants = 5%

In each case, multiply the number of panels produced by the percentage of defective panels.

`\begin{gathered} (2\%\text{ of b)+(6}\%\text{ of }24000)=5\%\text{ of (24000+b)} \\ 0.02b+0.06\mleft(24000\mright)=0.05\mleft(24000+b\mright) \end{gathered}`

We solve the equation for b.

`\begin{gathered} 0.02b+1440=1200+0.05b \\ \text{Combine like terms} \\ 1440-1200=0.05b-0.02b \\ 240=0.03b \\ b=(240)/(0.03) \\ b=8000 \end{gathered}`

Thus, 8000 panels were produced by Plant B.