SOLUTION: Cows cost $10, pigs cost $3 and chickens cost $0.50. A man buys 100 animals for $100. How many of each animal does he have? he must have at least one of each animal.

Question 108884: Cows cost $10, pigs cost $3 and chickens cost $0.50. A man buys 100 animals for $100. How many of each animal does he have? he must have at least one of each animal.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Cows cost $10, pigs cost $3 and chickens cost $0.50. A man buys 100 animals for $100. How many of each animal does he have? he must have at least one of each animal.
:
Let x = no. of cows
Let y = no. of pigs
Let z = no. of chicks
:
The no. of animal equation:
x + y + z = 100
:
The cost of animals equation
10x + 3y + .5z = 100
:
Multiply above equation by 2 and subtract the 1st equation:
20x + 6y + 1z = 200
x + y + z = 100
----------------------subtracting eliminates z
19x + 5y = 100
:
We know that x and y are integers; 19x and 5y have to be multiples of 5:
That leaves the only value we can have for x is 5
:
5 cows
:
19(5) + 5y = 100
95 + 5y = 100
5y = 100-95
5y = 5
y = one lonesome pig
:
5 cows and 1 pig would leave us with 94 chickens
:
Check our solutions in the cost equation
10(5) + 3(1) + .5(94) =
50.00 + 3.00 = 47.00 = $100

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