How many panels did plant B produced?

Question

Two factory plants are making TV panels. Yesterday, Plant A produced 4 times as many panels as Plant B. Four 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 two plants together produced 1440 defective panels?

Answer 1

Hello Melyssa!

 

Whenever I'm trying to solve a word problem line this, I like to start by making a table or by drawing a picture.  I do this so I can organize what I know - the organization helps me solve the problem.

 

After reading this problem, I'd start with a table.  Please draw out a table as explained below, as you read through how I solved this problem.

 

This table would have one row of info for Plant A, one row of info for Plant B, and one row of info for both plants combined.  I'd make these separate rows because the problem statement provides different kinds of information for Plant A, Plant B, and both plants combined.

 

One of the relationships I know for plant A and plant B, is that plant A produced 4 times as many panels as plant B did.  I don't know how many panels plant B produced, but I do know that if plant B produced "B" panels, then plant A produced 4B panels.  The total number of panels produced by both plants combined was 4B + B = 5B, where B is still unknown.  I'm going to put this information into the first column of data in our table.  This first column will be called "total number of panels produced".  For this column, 4B goes in for plant A, B goes in for plant B, and 5B goes in this column for both plants combined.

 

The next thing I know is that 4% of the panels from plant A are defective. When working with percents, you need to be able to convert them into decimal ... 4% is the same as 0.04 decimal (just like 4 cents is the same as 0.04 dollars).

 

I don't know how many panels were produced by plant A at this point, but I do know that the number is equal to 4B.  Therefore, the number of defective panels produced by plant A is 0.04 times 4B, or 0.16B.

 

I also know that 2% of the panels from plant B are defective.  Using the same kind of logic, 2% of B panels is 0.02B for plant B.

 

Combining all these pieces of information, my next column in the table will be the number of defective panels produced.  This column will have 0.16B defective panels for plant A, will have 0.02B defective panels for plant B, and will have 1440 defective panels for both plants combined.

 

At this point, you might notice that (the number of defective panels from plant A) + (the number of defective panels from plant B) = 1440.  From our table we can read these off:  0.16B + 0.02B = 1440, or 0.18B = 1440.  Because 0.18B = 1440, then B = 1440/0.18 = 8000.

 

Now that we know a value for B, we can solve the problem!  Plant B produced B = 8000 panels total.

 

Now that we know B, we could evaluate the other cells in the table to find out the number of panels produced by plant A (which would be 4 times 8000), or for any of the other cells as well.

 

Hope this solution process helps ...

 

Best regards,

William S.

 

 

Answer 2

Let x be the number of panels produced from Plant B.

Let 4x be the number of panels produced from Plant A. (since Plant A produced 4 times as many panels as Plant B)

 

Defective panels from Plant B is 0.02x (2%)

Defective panels from Plant A is 0.04(4x) = .16x (4%)

 

Two plants together produced 1440 defective panels:  

 0.02x +0 .16x = 1440

                                                                                           

 0.18x  = 1440

                                                                                                 

 x  = 8000   (Answer : Plant B produced 8000 panels)

 

Verify Answers:

Plant B produced 8000 panels and Plant A produced 32,000 panels.

2% panels produced by Plant B is 160, which is defective.

4% panels produced by Plant A is 1280, which is defective.

Sum up 160 and 1280 is equal to 1440 defective panels from both plants.