3 ducks and 1 chick cost the same as 2 geese. one duck, 2 chicks, and 3 geese cost $25. what is the price of each?

i get:

3d+c=2g
d+2c+3g=$25

i'm stuck from there. is there something missing? thanks in advance for any help.

Three unknowns, only two equations. Something else needs to be known.

Cool!

thanks for the really quick answer.

To solve this problem, you have two equations:

Equation 1: 3d + c = 2g
Equation 2: d + 2c + 3g = $25

You're correct in setting up these equations based on the given information. Now, we need to solve these equations simultaneously to find the price of each item.

To eliminate one variable, we can multiply Equation 1 by 3 and Equation 2 by 2 to create matching coefficients for 'g'. This will allow us to eliminate 'g' by subtracting the equations.

So, let's multiply Equation 1 by 3:

Equation 3: 9d + 3c = 6g

Now, let's multiply Equation 2 by 2:

Equation 4: 2d + 4c + 6g = $50

Next, subtract Equation 4 from Equation 3:

(9d + 3c) - (2d + 4c + 6g) = (6g - 6g) + ($50 - $50)

Simplifying, we get:

7d - c = 0

Now, we have a new equation:

Equation 5: 7d - c = 0

We can rearrange Equation 5 to solve for 'c':

c = 7d

Now, substitute this value of 'c' in Equation 1:

3d + c = 2g
3d + 7d = 2g
10d = 2g
g = 5d

Now that we have expressions for 'c' and 'g' in terms of 'd', we can substitute them in Equation 2:

d + 2c + 3g = $25
d + 2(7d) + 3(5d) = $25
d + 14d + 15d = $25
30d = $25
d = $25 / 30
d = $5/6

Now, we can substitute this value of 'd' to find 'c' and 'g':

c = 7d
c = 7 * ($5/6)
c = $35/6

g = 5d
g = 5 * ($5/6)
g = $25/6

Finally, we have the prices:

Duck (d) = $5/6
Chick (c) = $35/6
Goose (g) = $25/6

So, the price of each item is $5/6 for a duck, $35/6 for a chick, and $25/6 for a goose.