Problem solving

Question

Old Macdonald has a total of 100 chickens and goats in the barnyard. If he counts 286 feet altogether how many chickens and how many goats does Old Macdonald have ? how Can I solve this problem without using algebra ? 

Answer 1

you have 2 relationships so you need two equations:

1: chicken+goats=100, or:

c+g=100,

2: chickens have 2 legs and goats have 4, so since the number of feet =286:

2c+4g=286

multiply the first equation by 2 to solve using elimination:

2*(c+g=100)=2c+2g=200

subtract the new first equation from the second to get:

2g=86, or

g=43, and

the number of chickens =100-43=57

 

check:

2c+4g=286

2*57+4*43=286