Question 198277: It costs $5 for a cock,$3 for a hen and $1 for three chickens.By using $100
to buy 100 chicks,how many cocks,hens and chickens can we get?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! It costs $5 for a cock,$3 for a hen and $1 for three chickens.By using $100
to buy 100 chicks, how many cocks,hens and chickens can we get?
:
x = no. of cocks
y = no. of hens
z = no. of chickens
:
Total chick equation
x + y + z = 100
:
Cost equation
5x + 3y +  z = 100
Multiply by 3 to get rid of the denominator
15x + 9y + 1z = 300
:
subtract the 1st equation from the above equation:
15x + 9y + z = 300
x + y + z = 100
------------------
14x + 8y = 200
simplify, divide by 2
7x + 4y = 100
4y = 100 - 7x
y =  -  x
y = 25 - x
x has to be an integer that is a multiple of 4. Can only be 4, 8, or 12
remember that the number of chickens must be a multiple of 3. (3 for a $)
The sum of x & y subtracted from 100, has to be a multiple of 3
The leaves us: x=12, y=4, 100 - 12 - 4 = 84
:
Solution: 12 cocks, 4 hens, and 84 chickens
:
:
Check solution in cost equation:
5(12) + 3(4) + 84 =
60 + 12 + 28 = 100
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