The average weight of A, B and C is 45 Kg. If the average weight of A and B be 40 Kg and that of B and C be 43 Kg, weight of B is

The average weight of A, B and C is 45 Kg. If the average weight of A and B be 40 Kg and that of B and C be 43 Kg, weight of B is

To find the weight of B, approach the problem by setting up equations based on the average weights given

Let A, B, and C denote the weights of individuals A, B, and C respectively. According to the problem

The average weight of A, B, and C is 45 kg

A + B + C = 45 x 3 = 135

The average weight of A and B is 40 kg

A + B = 40 x 2 = 80

The average weight of B and C is 43 kg

B + C = 43 x 2 = 86

To find B's weight, we solve these equations step-by-step

From equation (2), we know

A + B = 80

From equation (3), we know

B + C = 86

Now, add equations (2) and (3) together to find

A + 2B + C = 80 + 86 = 166

From equation (1), we have

A + B + C = 135

Subtract equation (1) from previous one

A + 2B + C - (A + B + C) = 166 - 135

B = 31

Therefore, the weight of B is 31 Kg.

How to Calculate Average Weight Problems?

Average weight problems are common in mathematics, particularly in statistics and arithmetic. These problems involve calculating the average or mean weight of individuals or objects based on given data points or conditions.

Definition and Calculation of Average:

The average weight of a group of individuals or objects is calculated by dividing the total weight of all items by the number of items. This formula is fundamental to understanding how averages are derived in weight problems.

Formulating Equations:

In average weight problems involving multiple individuals, equations are often set up based on the relationships between the average weight of the group and the weights of individuals or subgroups within it. These equations help in deriving specific values when given partial information about the group.

Solving for Unknowns:

Typically, these problems involve finding the weight of one or more individuals when their combined average is known, along with averages of specific subgroups. Solving involves algebraic manipulation of equations to isolate and determine the unknown weights.

Mathematical Tools:

To solve average weight problems effectively, mathematical tools like algebra, arithmetic operations, and sometimes basic statistics are employed. These tools enable precise calculation and verification of solutions.

Applications:

Average weight problems are not just theoretical but find practical applications in various fields such as health sciences, finance, and manufacturing. For instance, calculating the average weight of products in a shipment helps in logistics planning and quality control. Beyond calculations, solving average weight problems enhances conceptual understanding of arithmetic and algebraic principles such as equations, averages, and relationships between different quantities.