On a farm, the number of chickens was more than the number of ducks. After 20% of the chickens were sold, there were 800 less chickens than ducks on the farm. How many ducks were there on the farm? ___ducks

1 Answer
Jul 7, 2018

#d = (4000 +4x)# where #x# is an integer greater than 0

Explanation:

#c > d# .......................................... (1)

#d - (c -20/100c)= 800# ..............(2)

so from (2)
#d - 0.8c= 800#

multiply through by 5 to get whole numbers

#5d - 4c = 4000#

#5d -4000 = 4c#

#4c = 5d -4000 #

#c = (5d -4000)/4 #

#c = (5d)/4 -4000/4 #

#c = (5d)/4 -1000# .........................(3)

substitute for c in (1).

#1.25d -1000 > d#

#1.25d -d -1000 +1000 > d - d +1000#

#0.25d > 1000#

#d > 4000#

but c must be a whole number so
in eqn (3) the term #(5d)/4# must be a whole number,
so #d# must be divisible by 4.

Combining both of these conditions gives:

#d = 4000 +4x# where #x# is an integer greater than 0