Systems of equations

Question

I bought some dogs and octopi.  Each dog costs $100 and each octopus cost $200. I paid a total of $2000 and got a total of 80 legs.  How many of each did I get?  

Please show work 

Answer 1

D = # of dogs

C = # of octopi

 

4D + 8C = 80

100D + 200C = 2000

 

multiply the top equation by 25

 

100D + 200C = 2000

100D + 200 C = 2000

 

now subtract equations

 

0 = 0

 

this system of equations is dependent, many, many answers

 

as long as D = (80-8C)/4 and is a positive integer it will work

 

for example, let's say you bought 5 Octopi   then D = (80-40)/4 =10

 

5 Octopi would have 40 legs and 10 dogs would have 40 legs, total 80 legs and try 

 

10 octopi  we would have 0 dogs

 

the price equation will check out as well

 

how many answers are there?

 

try to figure out the rest. there are a few more