Question 290584: A farmer ordered 100 animals for 100 dollars from a local mill. he knew he ordered some pigs, calves and chicks but he lost his receipt and forgot how many of each he orderd, he knew pigs were $3 each calves $10 each and chicks $.50 each. using this information determine what the farmers order was.
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! A farmer ordered 100 animals for 100 dollars from a local mill.
he knew he ordered some pigs, calves and chicks but he lost his receipt and
forgot how many of each he orderd,
he knew pigs were $3 each calves $10 each and chicks $.50 each.
using this information determine what the farmers order was.
:
Let c = no. of calves; p = no. of pigs; s = no. chickens
:
No. of animals equation:
c + p + s = 100
:
Calves cost $10, Pigs cost $3, and chickens cost $.50.
the $$ equation:
10c + 3p + .5s = 100
:
We have two equations but 3 unknowns, however, we know there can't very many calves,
After trying a couple values for no. of cows, came up with 5 cows,
they're worth $50, our two equations then are:
:
p + s = 100 - 5
p + s = 95
and
3p + .5s = 100 - 50
3p + .5s = 50
:
Multiply the 1st equation by 3 and subtract the 2nd equation:
3p + 3s = 285
3p + .5s = 50
---------------- subtracting eliminates p
0p + 2.5s = 235
s = 
s = 94 chickens
:
Find pigs
p + 94 = 95
p = 95 - 94
p = 1 pig
:
We have then: 5 calves, 1 pig, 94 chicken
;
;
Check in the cost equation
10(5) + 3(1) + 94(.5) =
50 + 3 + 47 = $100
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