The average weight of A, B, and C is 45. The average weight of A and B is 40, and the average of B and C is 43. Find the weight of B.

Steps to Solve

1. Set up the equations based on averages

Let the weights of A, B, and C be denoted as $A$, $B$, and $C$, respectively.

From the problem, we know:

• The average weight of A, B, and C is 45: $$ \frac{A + B + C}{3} = 45 $$

• The average weight of A and B is 40: $$ \frac{A + B}{2} = 40 $$

• The average weight of B and C is 43: $$ \frac{B + C}{2} = 43 $$

2. Rewrite the equations

From each average equation, we can derive the total weights:

• From the first equation: $$ A + B + C = 135 , (1) $$

• From the second equation: $$ A + B = 80 , (2) $$

• From the third equation: $$ B + C = 86 , (3) $$

3. Substitute and solve

Now, subtract equation (2) from equation (1): $$ (A + B + C) - (A + B) = 135 - 80 $$ This simplifies to: $$ C = 55 , (4) $$

Next, substitute $C$ back into equation (3): $$ B + 55 = 86 $$ Thus, we find: $$ B = 31 , (5) $$

Finally, substitute $B$ into equation (2) to find $A$: $$ A + 31 = 80 $$ This results in: $$ A = 49 , (6) $$

4. Conclusion

The weight of B is determined as follows: From equation (5), we have $B = 31$.