Question

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

Answer 1

`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