SOLUTION: Two factory plants are making TV panels. Yesterday, Plant A produced 24,000 panels. Six percent of the panels from Plant A and 2% of the panels from Plant B were defective.

Question 1098426: Two factory plants are making TV panels. Yesterday, Plant A produced
24,000
panels. Six 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 overall percentage of defective panels from the two plants was
5%
Found 4 solutions by josmiceli, ikleyn, MathTherapy, greenestamps:
Answer by josmiceli(19441)   (Show Source): You can put this solution on YOUR website!
Let = the number of panels
plant B produced
= number of
defective panels from plant A
= number of defective
panels from plant B
----------------------------------
AMP Parsing Error of [ { 1440 + .02b ) / ( 24000 + b ) = .05 ]: Invalid expression '{1440+.02\b)/(24000+b)=.05': syntax error at /home/ichudov/project_locations/algebra.com/templates/Algebra/Expression.pm line 203. .

Plant B produced 41,333 panels
-------------------------------
check the math and get a 2nd opinion if needed

Answer by ikleyn(52795)   (Show Source): You can put this solution on YOUR website!
.

0.06*24000 + 0.02*b = 0.05*(24000+b) (counting defective panels) ====> 1440 + 0.02b = 0.05*24000 + 0.05*b 1440 + 0.02b = 1200 + 0.05*b 1440 - 1200 = 0.05b - 0.03b 240 = 0.03b ====> b = = 8000. Answer. Plant B produces 8000 panels. Check. 0.06*24000 + 0.02*8000 = 1600; 0.05*(24000+8000) = 1600. ! Correct !

Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
Two factory plants are making TV panels. Yesterday, Plant A produced
24,000
panels. Six 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 overall percentage of defective panels from the two plants was
5%

Defective panels from Plant A: .06(24,000) = 1,440
With 2% of Plant B's and 1,440 of Plant A's panels being defective, and 5% of the total panels (Plant A + Plant B) being defective, we get: .02B + 1,440 = .05(B + 24,000)
.02B + 1,440 = .05B + 1,200
.02B - .05B = 1,200 - 1,440
- .03B = - 240
Number of panels produced by Plant B, or
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!

You have received three previous solutions to your problem, all using the formal algebraic method for solving this kind of problem. (and with one of those three solutions being wrong because of an arithmetic error...)

Here is an alternative method for solving this kind of problem which, if you understand it,will get you to the answer much faster and with much less work.

(1) The overall percentage of defective panels, 5%, is "three times as close" to the 6% of plant A as it is to the 2% of plant B:
;

(2) Therefore, plant A is producing three times as many panels as plant B.

(3) Since plant A is producing 24,000 panels, plant B is producing 8,000 panels.

Compare the amount of work required here with the amount required in the earlier solutions you received....
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