To solve the problem step by step, we will break it down as follows:
### Step 1: Find the total weight of A, B, and C
Given that the average weight of A, B, and C is 55 kg, we can calculate the total weight of A, B, and C using the formula for average:
\[
\text{Total weight of A, B, and C} = \text{Average} \times \text{Number of persons}
\]
\[
\text{Total weight} = 55 \, \text{kg} \times 3 = 165 \, \text{kg}
\]
### Step 2: Set up equations based on the relationships given
Let the weight of C be \( X \). According to the problem:
- C is 10 kg more than A: \( C = A + 10 \) or \( A = C - 10 \)
- C is 5 kg more than B: \( C = B + 5 \) or \( B = C - 5 \)
Substituting \( C \) with \( X \):
- \( A = X - 10 \)
- \( B = X - 5 \)
### Step 3: Write the equation for the total weight
Now we can express the total weight of A, B, and C in terms of \( X \):
\[
A + B + C = (X - 10) + (X - 5) + X = 165
\]
Combining the terms:
\[
3X - 15 = 165
\]
### Step 4: Solve for X
Now, we will solve for \( X \):
\[
3X = 165 + 15
\]
\[
3X = 180
\]
\[
X = 60 \, \text{kg}
\]
So, the weight of C is 60 kg.
### Step 5: Find the weights of A and B
Now we can find the weights of A and B using the value of \( X \):
\[
A = X - 10 = 60 - 10 = 50 \, \text{kg}
\]
\[
B = X - 5 = 60 - 5 = 55 \, \text{kg}
\]
### Step 6: Find the weight of D
According to the problem, D's weight is 19 kg more than C's weight:
\[
D = C + 19 = 60 + 19 = 79 \, \text{kg}
\]
### Step 7: Calculate the total weight of A, B, C, and D
Now we can find the total weight of A, B, C, and D:
\[
\text{Total weight of A, B, C, and D} = A + B + C + D = 50 + 55 + 60 + 79
\]
Calculating this:
\[
50 + 55 = 105
\]
\[
105 + 60 = 165
\]
\[
165 + 79 = 244 \, \text{kg}
\]
### Step 8: Find the average weight of A, B, C, and D
Finally, we can find the average weight:
\[
\text{Average weight} = \frac{\text{Total weight}}{\text{Number of persons}} = \frac{244}{4} = 61 \, \text{kg}
\]
### Conclusion
The average weight of A, B, C, and D is **61 kg**.
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