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:
[tex]x=4y[/tex]
We also know that 5% of panels produced by plant A are defective, this can be express as:
[tex]0.05x[/tex]
3% of panels produced by plant B are defective, this can be express as:
[tex]0.03y^{}[/tex]
And we know that the sum of defective panels is equal to 2530, then we have:
[tex]0.05x+0.03y=2530[/tex]
Hence we have the system of equations:
[tex]\begin{gathered} x=4y \\ 0.05x+0.03y=2530 \end{gathered}[/tex]
To solve it we plug the value of x from the first equation into the second one and solve for y:
[tex]\begin{gathered} 0.05(4y)+0.03y=2530 \\ 0.2y+0.03y=2530 \\ 0.23y=2530 \\ y=\frac{2530}{0.23} \\ y=11000 \end{gathered}[/tex]
Since y is the number of panels plant B produced we conclude that plant B produced 11,000 panels.
