Find the number of birds?

Question

We have 100 birds ..(Chickens , goeses , and Ducks)...
Suppose that a chicken costs ¢50, goes costs $3 and Duck costs $5 ...How many Chickens , goeses and ducks we can buy with $ 100 ????

Answer 1

Start with say ducks only. You can get 20. Now you decide what else you want. You can exchange a duck for 10 chickens or you can give up 3 ducks and collect 5 geese and so on

Answer 2

Are you saying you need to purchase 100 birds?
Then
84 chickens, 11 goeses, 5 ducks
84+11+5 = 100 and
.5(84) + 3(11) + 5(5)
= 42 + 33 + 25
= 100
Another:
88 chickens, 2 goeses, 10 ducks
Another:
80 chickens, 20 goeses, 0 ducks
I used the equations:
x + y + z = 100 and
.5x + 3y + 5z = 100
x = chickens, y = goeses, and z = ducks
then I eliminated the variable y
Multiply the first equation by -3 and then add that to the second equation
-3x - 3y - 3z = -300
.5x + 3y + 5z = 100
-2.5x +2z = -200
Now Multiply this equation by -2/5 (which is the reciprocal of
-2.5 = -5/2)
x - (4/5)z = 80
Now take the original two equations and cancel the x's
Multiply the first equation by -.5 and then add that to the second equation.
-.5x - .5y - .5z = -50
.5x + 3y + 5z = 100
2.5y + 4.5z = 50
Divide each side by 2.5 (so multiply by 2/5)
y + (9/5)z = 20
Now you have the equations
x - (4/5)z = 80 and
y + (9/5)z = 20
z must be a multiple of 5 (otherwise you will have fractions)
I substituted in z = 5, 10 , 0 (respectively, to get the above answers)

Answer 3

you can buy 40 chickens, 10 geese and 10 ducks for $100

Answer 4

40 chickens, 10 ducks, and 10 geese.

Answer 5

too many possibilities, make a graph