SOLUTION: Two factory plants are making TV panels. Yesterday, Plant A produced 6000 fewer panels than Plant B did. Three percent of the panels from Plant A and 4% of the panels from Plant B

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Question 1196657: Two factory plants are making TV panels. Yesterday, Plant A produced 6000 fewer panels than Plant B did. Three percent of the panels from Plant A and 4% of the panels from Plant B were defective. How many panels did Plant B produce, if the two plants together produced 800 defective panels?
Found 2 solutions by math_tutor2020, MathLover1:
Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

x = number of panels from plant B
x-6000 = number of panels from plant A

3% of (x-6000) = 0.03(x-6000) = number of defective panels from plant A
4% of x = 0.04x = number of defective panels from plant B

0.03(x-6000)+0.04x = total number of defective panels
0.03(x-6000)+0.04x = 800
0.03x-180+0.04x = 800
0.07x-180 = 800
0.07x = 800+180
0.07x = 980
x = 980/0.07
x = 14000 panels from plant B
x-6000 = 14000 - 6000 = 8000 panels from plant A

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Check:
3% of A = 0.03*8000 = 240 defective panels from A
4% of B = 0.04*14000 = 560 defective panels from B
240+560 = 800 defective panels total
The answer is confirmed.
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Answer: 14000 panels were produced by plant B.

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!


let the number of TV panels plant A produced be a, and the number of TV panels plant B produced be b
if plant A produced 6000 fewer panels than Plant B did, we have
a=b-6000........eq.1
if 3 percent of the panels from Plant A were defective , we have 0.03a defective panels
if 4% of the panels from Plant B were defective, we have 0.04b defective panels
if the two plants together produced 800 defective panels, we have
0.03a%2B0.04b=800......eq.2
sabstitite a from eq.1
0.03%28b-6000%29%2B0.04b=800......eq.2, solve for b

0.03b-180%2B0.04b=800
0.07b=800%2B180
0.07b=980
b=980%2F0.07
b=14000
go to
a=b-6000........eq.1, substitute b
a=14000-6000
a=8000
Plant A produced 8000 and Plant B produced 14000 panels.
check the number of defective panels:
Plant A produced 0.03%2A8000=240 defective panels
Plant B produced 0.04%2A14000=560
total:240%2B560=800 which confirms our results