Question

Solving a percent mixture problem using a linear equationSamantha VEspañolTwo factory plants are making TV panels. Yesterday, Plant A produced twice as many panels as Plant B. Two percent of the panels from Plant A and 3% of thepanels from Plant B were defective. How many panels did Plant B produce, if the two plants together produced 490 defective panels?

Answer 1

We are given a question about factory plants making TV panels. The following information holds.

Plant A produces twice as many panels as plant B. This can be expressed mathematically as:

`A=2B`

Also, 2% and 3% of the TV panels from Plant A and Plant B are defective, and both plants produced a total of 490 defective panels. This can be expressed mathematically as:

`(2A)/(100)+(3B)/(100)=490`

We can clearly see that we have derived two equations. We will substitute the first equation in the second equation to get the number of panels Plant B produced.

`\begin{gathered} (2(2B))/(100)+(3B)/(100)=490 \\ (4B)/(100)+(3B)/(100)=490 \\ (7B)/(100)=490 \\ \text{Cross multiply} \\ 7b=490*100 \\ B=(490*100)/(7) \\ B=70*100 \\ B=7000 \end{gathered}`

Therefore, the number of panels that plant B produced is:

ANSWER: 7000