The average weight of A, B and C is 50 kgs. The weight of B is 20 kgs less than A's weight and 5 kgs more than C's weight. What will be the average weight of A, B, C and D, if D we... The average weight of A, B and C is 50 kgs. The weight of B is 20 kgs less than A's weight and 5 kgs more than C's weight. What will be the average weight of A, B, C and D, if D weighs 2 kgs more than C?
Understand the Problem
The question is asking to calculate the average weight of individuals A, B, C, and D based on the provided relationships between their weights. We'll need to establish equations based on the average weight given and the relationships outlined.
Answer
The average weight of A, B, C, and D is $48$ kg.
Answer for screen readers
The average weight of A, B, C, and D is $48$ kg.
Steps to Solve
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Identify given information We know the average weight of A, B, and C is 50 kg. Therefore, we can establish the equation:
$$ \frac{A + B + C}{3} = 50 $$
Multiplying both sides by 3 gives:
$$ A + B + C = 150 $$ -
Establish relationships based on the problem From the problem statement, we have the following relationships:
- Weight of B is 20 kg less than A:
$$ B = A - 20 $$ - Weight of B is 5 kg more than C:
$$ B = C + 5 $$
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Substituting B in terms of A and C Substituting the first equation into the second gives:
$$ A - 20 = C + 5 $$
Rearranging this, we can express C in terms of A:
$$ C = A - 25 $$ -
Substituting C back into the equation for A, B, C Now we substitute C back into the equation $ A + B + C = 150 $:
$$ A + (A - 20) + (A - 25) = 150 $$
Simplifying this gives:
$$ 3A - 45 = 150 $$ -
Solving for A Adding 45 to both sides:
$$ 3A = 195 $$
Dividing by 3 gives:
$$ A = 65 $$ -
Finding B and C Now we can find B and C using the established relationships:
- For B:
$$ B = A - 20 = 65 - 20 = 45 $$ - For C:
$$ C = A - 25 = 65 - 25 = 40 $$
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Finding D's weight If D weighs 2 kg more than C:
$$ D = C + 2 = 40 + 2 = 42 $$ -
Calculating the average weight of A, B, C, and D Now we can calculate the average weight:
$$ \text{Average} = \frac{A + B + C + D}{4} = \frac{65 + 45 + 40 + 42}{4} $$
Calculating the numerator:
$$ 65 + 45 + 40 + 42 = 192 $$
Thus, the average is:
$$ \text{Average} = \frac{192}{4} = 48 $$
The average weight of A, B, C, and D is $48$ kg.
More Information
This problem involves setting up equations based on relationships between different variables and solving them systematically. The average weight calculation involves basic arithmetic operations after determining individual weights.
Tips
- Misinterpreting relationships: Carefully relate the weights of B and C to A to avoid confusion.
- Arithmetic errors: Double-check calculations when summing weights and calculating averages to prevent mistakes.
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