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Production records indicate that the number of defective tennis balls produced on a...

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cbromm | (Level 1) Honors

Posted July 10, 2013 at 12:09 AM via web

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Production records indicate that the number of defective tennis balls produced on a certain production line is related by a linear equation to the total number produced.  Suppose this is true.  If 7 defective balls are produced in a total of 450 in one day and 33 defective balls are produced in a total of 1075 on another day, then how many defective tennis balls will be expected on a day when the total production is 1260?

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llltkl | College Teacher | (Level 3) Valedictorian

Posted July 10, 2013 at 2:07 AM (Answer #1)

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The number of defective tennis balls produced on a certain production line is related by a linear equation to the total number of balls produced.  

Let the number of defective tennis balls produced be y, and the total number of balls produced be x.

Then their relationship is one of the type

y=ax+b, where a and b are constant quantities.

Putting the corresponding values of the days mentioned here, two equations are obtained such that,

        7=450a+b --- (i)

and 33=1075a+b --- (ii)

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(ii)-(i), 26=625a

`rArr` a=26/625 = 0.0416

Putting this value of a in eq. (i),

450*0.0416+b=7

`rArr` b=7-18.72=-11.72

So, the production related equation takes the form,

y=0.0416x-11.72

Putting x=1260 in this equation we get,

y=1260*0.0416-11.72 = 40.7

= 41 (approximately).

Therefore, number of defective tennis balls expected on a day when the total production is 1260, is 41.

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