A farmer buys 100 live animals for $100. How many of each does he buy if chicks are 10 cents each pigs are $2 each and sheep are $5 each

Question

how many in total

 

Answer 1

We'll let S be the free variable

 

C+P+S = 100

 

10C + 200P + 500S = 10000 <--- amounts in pennies

 

C + 20P + 50S = 1000

 

C+P = 100 - S

 

C + 20P = 1000 - 50S

 

20P - P = 1000 - 50S - 100 + S

 

19P = 900-49S

 

P = (900-49S)/19

 

 

C + P + S = 100

 

C = 100 - s - P

 

   = 100 - s - (900-49S)/19

 

 

One possible combination that produces integers amounts of each livestock is:

11 sheep, 70 chicks, and 19 pigs