SOLUTION: A farmer went to the market and bought 100 animals. Each chicken cost .10 cents, pigs cost $2.00 and sheep cost $5.00. The farmer spent $100. How many of each animal did the farmer

Question 61824: A farmer went to the market and bought 100 animals. Each chicken cost .10 cents, pigs cost $2.00 and sheep cost $5.00. The farmer spent $100. How many of each animal did the farmer buy?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A farmer went to the market and bought 100 animals. Each chicken cost .10 cents, pigs cost $2.00 and sheep cost $5.00. The farmer spent $100. How many of each animal did the farmer buy?
:
number of animal equation:
c + p + s = 100
:
Cost equation
.1c + 2p + 5s = 100
:
Obviously the number of chickens has to be a multiple of 10, and quite a few of them (over 50) since the other animals are integer dollars
:
Write the equations with the chickens out of the picture:
2p + 5s = 100 - .10c
p + s = 100 - c
:
Tried 80, then 70 chickens viola!, the equations are then:
2p + 5s = 93
p + s = 30
:
Mult the 2nd equation by 2 and subtract:
2p + 5s = 93
2p + 2s = 60
------------
3s = 33
s = 33/3
s = 11 sheep
:
Use p + s = 30 to find p
p = 30 - 11
p = 19 pigs
:
Check our solutions
.10(70) + 2(19) + 5(11) = $100
70 + 19 + 11 = 100

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