There are three boys - A, B, and C in a family. The average weight of those three boys is 44 kgs. If the average weight of A and B is 39 kgs and that of A and C is 42 kgs. What is... There are three boys - A, B, and C in a family. The average weight of those three boys is 44 kgs. If the average weight of A and B is 39 kgs and that of A and C is 42 kgs. What is A's weight? (in kgs) Read more

Steps to Solve

1. Set Up the Equations from Averages

Let the weights of boys A, B, and C be represented as $a$, $b$, and $c$ respectively.

From the problem, we have the following averages:

• The average weight of A, B, and C:

$$ \frac{a + b + c}{3} = 44 $$

Multiplying through by 3, we get:

$$ a + b + c = 132 \quad (1) $$

• The average weight of A and B:

$$ \frac{a + b}{2} = 39 $$

Multiplying through by 2, we arrive at:

$$ a + b = 78 \quad (2) $$

• The average weight of A and C:

$$ \frac{a + c}{2} = 42 $$

Again, multiplying through by 2 gives:

$$ a + c = 84 \quad (3) $$

2. Solve for B and C in Terms of A

Using equation (2):

From $a + b = 78$, we can express $b$ in terms of $a$:

$$ b = 78 - a \quad (4) $$

Using equation (3):

From $a + c = 84$, we can express $c$ in terms of $a$:

$$ c = 84 - a \quad (5) $$

3. Substitute into Equation (1)

Now substitute equations (4) and (5) into equation (1):

$$ a + (78 - a) + (84 - a) = 132 $$

This simplifies to:

$$ 78 + 84 - a = 132 $$

4. Solve for A

Combining like terms, we have:

$$ 162 - a = 132 $$

Isolating $a$ gives:

$$ a = 162 - 132 $$

Thus:

$$ a = 30 $$

5. Final Result for A's Weight

We have found the weight of boy A:

$$ a = 30 \text{ kg} $$