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Denali and Nate work for a dog walking business and are paid for each dog they walk. Denali is responsible for 16 dogs and Nate is responsible for 12 dogs. Under the company's new policy, they will be assigned or unassigned new dogs in groups of x dogs. The ratio of Denali's pay to Nate's pay would be the same if Denali started walking 4x$ more dogs and Nate stayed at 12 dogs or if x of Nate's dogs were reassigned to Denali. Find x if x is not 0.

 Apr 21, 2019
 #1
avatar+104646 
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16 + 4x          16 + x

______    =    ______      cross - multiply

  12                  12 - x   

 

 

[  16 + 4x ] [ 12 - x ]   = 12 [ 16 + x ]      simplify

 

192 + 32x - 4x^2  =  192 + 12x      rearrange as

 

4x^2 - 20x  =  0

 

4x ( x - 5)   = 0

 

Only the second factor gives a non-zero   answer

 

x  = 5

 

Check

 

16 + 4(5)           16  + 5

________  =   ________

    12                 12 - 5

 

36            21

__   =     ___   =   3   .....so.....5 is good  !!!!

12             7

 

 

 

cool coolcool

 Apr 21, 2019

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