Three ducks and two ducklings weigh 32 kg. Four ducks and three ducklings weigh 44kg. All ducks weigh the same and all ducklings weigh the same. What is the weight of two ducks and one duckling?

20kgs?

3 D + 2 d = 32

4 D + 3 d = 44

multiply first by 3, second by 2

9 D + 6 d = 96
8 D + 6 d = 88 subtract
----------------
D = 8
so 3*8 + 2 d = 32
2 d = 8
d = 4
so
2(8) + 1(4) = 20

Thank You!

omg this is so useful thanks a lot

Well, if we let X represent the weight of a duck and Y represent the weight of a duckling, we can set up a system of equations. From the given information, we know that:

3X + 2Y = 32kg (equation 1)
4X + 3Y = 44kg (equation 2)

To find the weight of two ducks and one duckling, let's call that Z. In terms of X and Y, we have:

2X + Y = Z (equation 3)

Now, let's solve the system of equations to find the values of X, Y, and Z. Solving equations 1 and 2 simultaneously, we get X = 8kg and Y = 4kg.

Plugging these values into equation 3, we find:

2(8kg) + 4kg = Z
16kg + 4kg = Z
20kg = Z

So, the weight of two ducks and one duckling is indeed 20kg! Nice guess!

To solve this problem, we can set up a system of equations based on the given information. Let's assume that the weight of each duck is represented by 'D' and the weight of each duckling is represented by 'd'.

According to the given information:
Three ducks and two ducklings weigh 32 kg, so we can write the equation:
3D + 2d = 32 (Equation 1)

Four ducks and three ducklings weigh 44 kg, so we can write the equation:
4D + 3d = 44 (Equation 2)

To find the weight of two ducks and one duckling, we need to solve this system of equations.

Let's simplify Equation 1:
3D + 2d = 32

Multiply both sides of the equation by 2 to eliminate the fractional coefficient:
6D + 4d = 64 (Equation 3)

Now, we have two equations:
4D + 3d = 44 (Equation 2)
6D + 4d = 64 (Equation 3)

To solve this system of equations, we can use the method of substitution or elimination.

Let's use substitution method:
Solve Equation 2 for D:
4D = 44 - 3d
D = (44 - 3d)/4

Now substitute this expression for D in Equation 3:
6(44 - 3d)/4 + 4d = 64

Multiply both sides of the equation by 4 to eliminate the fractional coefficient:
6(44 - 3d) + 16d = 256

Simplify the equation:
264 - 18d + 16d = 256
-2d = -8

Divide both sides of the equation by -2:
d = -8 / -2
d = 4

Now that we have the value of d, we can substitute it back into Equation 2 to find the value of D:
4D + 3(4) = 44
4D + 12 = 44
4D = 44 - 12
4D = 32
D = 32 / 4
D = 8

So, each duck weighs 8 kg and each duckling weighs 4 kg.

To find the weight of two ducks and one duckling, we can substitute these values back into the equation:
2D + 1d = 2(8) + 1(4) = 16 + 4 = 20 kg.

Hence, the weight of two ducks and one duckling is 20 kg, not 20 kgs.

Why would you multiply it by two or three though?