+21 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.
+128475 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
