SOLUTION: I need a total of 100 birds from 3 different species.The total budget is 100 dollars.If the chickens cost .50 cents,the ducks 3 dollars and the turkeys 10 dollars,how many of each

Question 148017: I need a total of 100 birds from 3 different species.The total budget is 100 dollars.If the chickens cost .50 cents,the ducks 3 dollars and the turkeys 10 dollars,how many of each do I need to get the 100 birds with the 100 dollars budget?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
I need a total of 100 birds from 3 different species.The total budget is 100 dollars.If the chickens cost .50 cents,the ducks 3 dollars and the turkeys 10 dollars,how many of each do I need to get the 100 birds with the 100 dollars budget?
:
The 3 types of birds:
x = no. of chickens
y = no. of ducks
z = no. of turkeys
:
Total birds equation:
x + y + z = 100
:
total cost equation:
.50x + 3y + 10z = 100
:
We got two equationa and three unknowns, will have to use common sense here.
:
Multiply the above equation by 2, subtract the 1st equation from it
1x + 6y + 20z = 200
1x + 1y + 1z = 100
------------------------subtracting eliminates x
0x + 5y + 19z = 100
Arrange the equation like this
5y = 100 - 19z
Divide equation by 5
y = 20 - z
;
Look at this equation, y had to be a positive integer (no fractional or negative ducks)
That really limits the possible values for z.
:
Try an obvious value:
z = 5 turkeys
:
y = 20 - (5)
y = 20 - 19
y = 1 duck
:
Using these values, find x:
x + 1 + 5 = 100
x = 100 - 6
x = 94 chickens
:
Check solution in the cost equation
.50(94) + 3(1) + 10(5) =
47 + 3 + 50 =$100

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