Two factory plants are making TV panels.

Question

Two factory plants are making tv panels. Yesterday, Plant A produced 4000 fewer planets than Plant B did. Three percent of the panels from Plant A and 4 % of panels from Plant B were defective. How many panels did Plant B produce, if the two plants together produced 1070 defective panels?

Answer 1

Let's set up a series of equations to figure this out.

First, let's take the first part: "Plant A produced 4000 fewer panels than Plant B did." Let's say that A represents the number of panels that Plant A produced, and B represents the number of panels that Plant B produced. We can write the equation like so:

A = B – 4000

Now, let's take a look at the next part: "3% of the panels from Plant A and 4% of the panels from Plant B were defective." We can combine that knowledge with the last part of the problem: that "the two plants together produced 1070 defective panels." Let's write that equation:

0.03A + 0.04B = 1070

Now we have a series of two equations with two unknowns, A and B:

A = B – 4000

0.03A + 0.04B = 1070

If we plug B + 4000 into the second equation in place of A (since B + 4000 and A are equal to one another), we get:

0.03(B – 4000) + 0.04B = 1070

And now we solve for B:

0.03B – 0.03*4000 + 0.04B = 1070

0.07B – 120 = 1070

0.07B = 1190

B = 17000

We can check our answer by solving for A:

A = B – 4000

A = 17000 – 4000

A = 13000

And now we plug our values for A and B into the other equation as the check:

0.03A + 0.04B = 1070

0.03(13000) + 0.04(17000) = 1070

390 + 680 = 1070

1070 = 1070

Looks like it's all set! Therefore, our final answer is:

B = 17000

Answer 2