Uncertain Number of Persons in Seating A seating chart is presented with 10 numbered chairs, but some of the chairs are occupied by 3 people each, while othe...
A seating chart is presented with 10 numbered chairs, but some of the chairs are occupied by 3 people each, while others are empty. How many people are left free in the seating chart?
Solution:
There are two approaches to solving this problem:
1. Logic:
Imagine a seating chart with only 5 people. How many chairs would be empty?
Now imagine the same seating chart with 7 people. How many chairs would be occupied?
By systematically trying different combinations of occupied and empty chairs, we can find that there are 3 empty chairs in the seating chart.
2. Analytical:
Calculate the total number of chairs in the seating chart (10).
Calculate the number of occupied chairs (3).
Calculate the number of empty chairs by subtracting the occupied chairs from the total.
The answer is 7, which is the number of free chairs in the seating chart.
Examples:
If 5 people are sitting in chairs 1, 3, and 4, then chairs 2 and 5 are empty.
If 7 people are sitting in chairs 1, 2, 5, 6, and 7, then chairs 3, 4, and 6 are empty.
If 10 people are sitting in chairs 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10, then there are 3 empty chairs