farmer brown just bought 100 animals. He spent $600 but can't remember how many of each animal he bought. Geese are $21, guinea pigs are $8 and chooks are $3. He remembers he bought an even number of geese. How many of each did he buy?

Question

farmer brown just bought 100 animals.  He spent $600 but can't remember how many of each animal he bought.  Geese are $21, guinea pigs are $8 and chooks are $3.  He remembers he bought an even number of geese.  How many of each did he buy?

Steve · Accepted Answer

Facts as presented:
g+p+c = 100
21g+8p+3c=600

since c = 100-(g+p),
21g+8p+3(100-g-p) = 600
21g+8p+300-3g-3p = 600
18g+5p = 300

Since 5p = 300-18g, g must be a multiple of 5. But, since g is even, it must be 10,20,30,...

If g=10, p=24
If g=20, 18g=360, so any number g>10 will not work.

So, we have 10 geese, 24 pigs, and 66 chooks

Sally · Answer

So, we have 10 geese, 24 pigs, and 66 chooks