Find the number of panels produced by plant B:

Question

Two factory plants are making Tv panels. yesterday, plant A produce 4000 fewer panels than plant B did. Two percent of panels from Plant A and 5% of the panels B were detective. How many panels did plant B produce, if the two plants together produce 970 detective panels?

Answer 1

Hi Ali,

 

This is a great question that combines percentages and solving for variables.  Let's break this question down phrase by phrase.

 

1) plant A produce[d] 4000 fewer panels than plant B did - We can write this in math as A=B-4000 where A represents the number of panels produced by factory A and B represents the number of panels produced by factory B

 

2) Two percent of panels from Plant A and 5% of the panels B were de[f]ective - 2 percent is 0.02 and 5 percent is 0.05.  So if A_d and B_d represent the number of defective panels produced by factories A and B, respectively, then we can write

A_d = 0.02A

B_d = 0.05B

 

3) the two plants together produce 970 de[f]ective panels - this means that A_d+B_d=970

 

4) How many panels did plant B produce - To find B, we can substitute for variables in the equations that we already have.

A_d+B_d=970

Since we know what A_d and B_d are in equation form, we can write

0.02A+0.05B=970

We also know that A=B-4000.  So, we can substitute for A.

0.02(B-4000)+0.05B=970

Now, we can solve for B using algebra.

0.02(B-4000)+0.05B=970

0.02B-80+0.05B=970

0.07B-80=970

0.07B=1050

B=15,000