A small, medium, and large sized chicken were weighing themselves on a scale. The large and medium chicken steppedon the scale together with a total weight of 30 lbs. The large and small chicken had a total weight of 25 lbs. The small and medium chickens had a total weight of 13 lbs. What will the scale read when all three step on together? How much does each chicken weigh? Explain how you found your answer.

L+M=30

L+S=25
S+M=13

These are big chickens. Why didn't they weigh one at a time? I know, they were chicken.

subtract the second equation from the first:
M-S=5
now add the third equation
2M=18
M=9
you take it from there

To find the weight of each chicken and the total weight when all three chickens step on the scale together, we can set up a system of equations. Let's use L, M, and S to represent the weights of the large, medium, and small chickens, respectively.

From the given information, we have the following equations:

1. L + M = 30 (equation 1)
2. L + S = 25 (equation 2)
3. S + M = 13 (equation 3)

We can solve this system of equations to find the weights of each chicken:

1. Subtracting equation 2 from equation 1:
(L + M) - (L + S) = 30 - 25
L + M - L - S = 5
M - S = 5 (equation 4)

2. Adding equation 2 and equation 3:
(L + S) + (S + M) = 25 + 13
L + S + S + M = 38
L + 2S + M = 38 (equation 5)

Now we have two equations (equations 4 and 5) with two variables (M and S). Solving this system will give us the weights of the medium and small chickens.

3. Subtracting equation 4 from equation 5:
(L + 2S + M) - (M - S) = 38 - 5
L + 2S + M - M + S = 33
L + 3S = 33 (equation 6)

From equation 6, we can find L in terms of S:
L = 33 - 3S (equation 7)

Now, substituting equation 7 into equation 2:
(33 - 3S) + S = 25
33 - 3S + S = 25
33 - 2S = 25
-2S = 25 - 33
-2S = -8
S = -8 / -2
S = 4

Substituting the value of S into equation 7:
L = 33 - 3(4)
L = 33 - 12
L = 21

Thus, the weight of the small chicken (S) is 4 lbs, the weight of the medium chicken (M) is 9 lbs, and the weight of the large chicken (L) is 21 lbs.

To find the total weight when all three chickens step on the scale together, we simply add their weights:
Total weight = S + M + L = 4 + 9 + 21 = 34 lbs

Therefore, when all three chickens step on the scale together, the scale will read 34 lbs.

To find the weight of each chicken and the scale reading when all three step on together, we can solve this problem using a system of equations.

Let's assign variables to represent the weight of each chicken. Let L represent the weight of the large chicken, M represent the weight of the medium chicken, and S represent the weight of the small chicken.

From the given information, we have the following equations:

Equation 1: L + M = 30 (The large and medium chickens together weigh 30 lbs)
Equation 2: L + S = 25 (The large and small chickens together weigh 25 lbs)
Equation 3: S + M = 13 (The small and medium chickens together weigh 13 lbs)

We now have a system of three equations with three unknowns. We can solve this system using various methods, such as substitution or elimination. Here, we'll use elimination:

Step 1: Subtract Equation 2 from Equation 1:
(L + M) - (L + S) = 30 - 25
M - S = 5 (Equation 4)

Step 2: Subtract Equation 3 from Equation 1:
(L + M) - (S + M) = 30 - 13
L - S = 17 (Equation 5)

Now we have a new system of equations:

Equation 4: M - S = 5
Equation 5: L - S = 17

We can now solve this new system. Adding Equation 4 and Equation 5, we get:

(M - S) + (L - S) = 5 + 17
M + L - 2S = 22 (Equation 6)

Since we have three equations (Equation 4, Equation 5, and Equation 6) with three unknowns (L, M, and S), we can solve this system.

Now comes the clever part. Notice that Equation 6 gives us a relationship between the weights of the chickens without explicitly revealing their individual weights. We can think of it as a total weight equation.

The equation M + L - 2S = 22 implies that the total weight of all three chickens combined is 22 lbs. This means that when all three chickens step on the scale together, the scale will read 22 lbs.

To find the weight of each chicken individually, we can now substitute the value of L - S (which is 17, from Equation 5) into Equation 1:

L + M = 30
(L - S) + M = 30
17 + M = 30
M = 30 - 17
M = 13

We now know that the weight of the medium chicken is 13 lbs.

Substituting the values of M and S (both found now) into Equation 3, we can find the weight of the small chicken:

S + M = 13
S + 13 = 13
S = 13 - 13
S = 0

Finally, substituting the values of M and S (both found now) into Equation 2, we can find the weight of the large chicken:

L + S = 25
L + 0 = 25
L = 25 - 0
L = 25

Therefore, the weight of the large chicken is 25 lbs.

In summary:
- The scale will read 22 lbs when all three chickens step on together.
- The weight of the small chicken is 0 lbs.
- The weight of the medium chicken is 13 lbs.
- The weight of the large chicken is 25 lbs.

This solution is derived by using algebraic manipulation to solve the system of equations and deducing the relationships between the weights of the chickens.