Calculating the Weight of a New Person Replacing an Old One

When a new person replaces an old one in a group, the average weight of the group can change. This tutorial will explore how to calculate the weight of the new person based on the change in the average weight and the weight difference.

Concept of Average Weight and Change

The concept of average weight can be understood as the total weight of all the persons in a group divided by the number of persons. When a new person replaces one from the group, the total weight of the group might change, thereby altering the average weight. This phenomenon can be reversed to find the weight of the new person.

First Example:

The average weight of 8 people increases by 2.5 kg when a new person comes in place of one of them weighing 45 kg.

We can solve this problem as follows:

Calculate the increase in total weight: 2.5 kg per person for 8 people 20 kg. This means the total weight of the group increases by 20 kg. Use the formula: weight of the new person increase in total weight weight of the person replaced. 20 kg (increase in total weight) 45 kg (weight of the person replaced) 65 kg (weight of the new person).

This can be represented as:
2.5 x 8 20
20 45 65 kg

Second Example:

The average weight of 7 persons increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg.

Solving for the new person's weight follows similar steps:

Calculate the increase in total weight: 2.5 kg per person for 7 people 17.5 kg. This means the total weight of the group increases by 17.5 kg. Use the formula: weight of the new person increase in total weight weight of the person replaced. 17.5 kg (increase in total weight) 65 kg (weight of the person replaced) 82.5 kg (weight of the new person).

This can be represented as:
2.5 x 7 17.5
17.5 65 82.5 kg

Third Example:

The average weight of a group of 15 persons increases by 2 kg on the replacement of one person weighing 35 kg by another person.

The problem is solved in the following way:

Calculate the increase in total weight: 2 kg per person for 15 people 30 kg. This means the total weight of the group increases by 30 kg. Use the formula: weight of the new person increase in total weight weight of the person replaced. 30 kg (increase in total weight) 35 kg (weight of the person replaced) 65 kg (weight of the new person).

Thus, the weight of the new person can be calculated as:
2 x 15 30
30 35 65 kg

These examples illustrate the formula and steps for calculating the weight of a new person who replaces an old person in a given group, based on the change in the average weight of the group.

Keywords: average weight, weight increase, replacement person