There are certain number of benches in a class. If 4 students sit on one bench…

To solve this problem, we can use algebra by setting up equations based on the information provided.

Algebraic Analysis
Define Variables:

Let b be the total number of benches.

Let s be the total number of students.

Translate Statements into Equations:

Condition 1: "If 4 students sit on one bench then 1 bench remains unoccupied."

This means all students are seated on (b - 1) benches.

Therefore, the total number of students is: s = 4 * (b - 1), which simplifies to s = 4b - 4.

Condition 2: "If 3 students sit on one bench then 23 students remain standing."

This means 3 students are on each of the b benches, plus 23 extra students who have no seat.

Therefore, the total number of students is: s = 3b + 23.

Solve the Equations:

Since both expressions are equal to the total number of students (s), we can set them equal to each other:

4b - 4 = 3b + 23

Now, isolate the variable b by subtracting 3b from both sides:

b - 4 = 23

Add 4 to both sides:

b = 27

Now that we know there are 27 benches, substitute this value back into the second equation to find the total number of students (s):

s = 3 * 27 + 23

s = 81 + 23

s = 104