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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.

 Jan 1, 2020
 #1
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I'm getting x = 10.

 Jan 1, 2020
 #2
avatar+106519 
+1

We have that

 

16 +  4x           16  + x      

______   =    _________                      cross-multiply

   12                12   -   x

 

 

( 16 + 4x) ( 12 - x)  =  12 ( 16 + x)     simplify

 

192 + 48x - 16x  - 4x^2   =  192  + 12x       

 

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

 

4x^2  =  20x

 

4x^2 -  20x  +  0      factor

 

4x ( x - 5)  =  0

 

Only the second factor produces what we need

 

x  - 5   = 0

 

x  = 5

 

 

cool cool cool

 Jan 1, 2020

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