SOLUTION: Two factory plants are making TV panels. Yesterday, Plant A produced 5000 panels. Three percent of the panels from Plant A and 10% of the panels from Plant B were defective. How

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Two factory plants are making TV panels. Yesterday, Plant A produced 5000 panels. Three percent of the panels from Plant A and 10% of the panels from Plant B were defective. How       Log On


   

Question 1162248: Two factory plants are making TV panels. Yesterday, Plant A produced
5000 panels. Three percent of the panels from Plant A and 10% 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 2 solutions by solver91311, greenestamps:
Answer by solver91311(24713) About Me  (Show Source):
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Answer by greenestamps(13216) About Me  (Show Source):
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A solution using logical reasoning and simple arithmetic instead of formal algebra....

This is essentially a "mixture" problem, where you are mixing 3% and 10% and getting on overall average of 5%.

Consider the three averages of 3%, 5%, and 10% on a number line. The average percentage of 5% is 2% away from the 3% average of plant A and 5% away from the 10% average of plant B.

Since the overall average is closer to the average for plant A, more panels were produced in plant A than in plant B. And the distances of the 3% and 10% from the overall average of 5% mean that the ratio of the numbers of panels produced by plants A and B is 5:2.

Then, since 5000 were produced in plant A, the number produced by plant B was 2000.