Question

How many panels did plant B produce, if two plants together produced 2530 defective panels

Answer 1

Let x be the number of panels plant A produces and lat y be the number of panels plant B produces.

We knot that plant A produces 4 times as many panels as plant B, this means that:

`x=4y`

We also know that 5% of panels produced by plant A are defective, this can be express as:

`0.05x`

3% of panels produced by plant B are defective, this can be express as:

`0.03y^{}`

And we know that the sum of defective panels is equal to 2530, then we have:

`0.05x+0.03y=2530`

Hence we have the system of equations:

`\begin{gathered} x=4y \\ 0.05x+0.03y=2530 \end{gathered}`

To solve it we plug the value of x from the first equation into the second one and solve for y:

`\begin{gathered} 0.05(4y)+0.03y=2530 \\ 0.2y+0.03y=2530 \\ 0.23y=2530 \\ y=(2530)/(0.23) \\ y=11000 \end{gathered}`

Since y is the number of panels plant B produced we conclude that plant B produced 11,000 panels.