Find the number of birds?

Question

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

Answer 1

This is a problem that has multiple solutions and can be solved using multiple equations. I'll call the number of chickens bought C, the number of gooses bought G, and the number of ducks bought D. Since we have a budget of100 dollars and we know the prices of the birds we can set up an equation in terms of money...

---100 = 0.5*C + 3*G + 5*D

Since we also know we're going to buy 100 birds in total we can also set up an equation in terms of total birds bought...

---100 = C + G + D

The trick here will be to set both of these equations up using algebra so that one of the variables (I'll use the Chickens here) is alone for both sides...

---100 = 0.5*C + 3*G + 5*D
---200 = C + 6*G + 10*D
---C = 200 - 6*G -10*D

---100 = C + G + D
---C = 100 - G - D

Since we have two different equations that C equals, we can set the right side of both equations equal to each other, as below...

---200 - 6*G - 10*D = 100 - G - D
---100 = 5*G + 9*D

This final equation gives us all the valid combinations of ducks and geese that can be bought. If you can find a pair of numbers G and D such that the above equation holds, it should be a valid answer to the problem. Because buying a fraction of a bird is sick and twisted, I found three solutions using integers...

D=0, G=20 (C then equals 80)
D=5, G=11 (C then equals 84)
D=10, G=2 (C then equals 88)

So, using the second solution for example, we can see that 84+11+5=100, which is good because we wanted 100 total birds. We can also multiply the 84 chickens by half a dollar (42 dollars), the 11 geese by 3 dollars (33 dollars), and the 5 ducks by 5 dollars each (25 dollars). 42+33+25 = 100 dollars, so the solution holds. You can verify the other two solutions in a similar manner.

Answer 2

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

84 chickens, 11 goeses, 5 ducks
84+11+5 = 100 and
.5(84) + 3(11) + 5(5)
= 42 + 33 + 25
= 100

Answer 4

C = chickens
G = gooses
D = ducks

Formula is:

.5C + 3G + 5D = 100

There are dozens of solutions to this formula, here are a few:

D = 20; 20 ducks and no geese or chickens.
C = 200; 200 chickens and no ducks or geese.
D = 10, G = 10, C = 40; 10 ducks, 10 geese, and 40 chickens.

Answer 5

U can get 40 chickens, 10 gooses, and 10 ducks

Answer 6

divide .50 by 100 same with $3 and $5 each will give you how many you can get,,,,easy

Answer 7

84 - CHICKEN
11 - GOESES
5 - DUCKS