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?
:
x = no. of cocks
y = no. of hens
z = no. of chickens
:
Total chick equation
x + y + z = 100
:
Cost equation
5x + 3y + {{{1/3}}}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 = {{{100/4}}} - {{{7/4}}}x
y = 25 - {{{7/4}}}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) + {{{1/3}}}84 = 
60 + 12 + 28 = 100