Question

2. There are some benches in a classroom. If 4 students sit on each bench then 3 benches

Answer 1

Answer: There are 48 students in the class.

Step-by-step explanation:

Let the number of students = S

Let the number of benches = B

If 4 students sit on each bench, 3 benches are left vacant.

S = 4(B - 3)

S = 4·B - 12 } Equation 1

If 3 students sit on each bench, 3 students still standing.

S = 3·B + 3 } Equation 2

We can match the two equations because they both indicate the same number of students.

4B - 12 = 3·B + 3

on solving this

4·B - 3·B = 3 + 12

B = 15 → number of benches

That is the number of benches, therefore substituting the value for B in equation 1

S = 4·B - 12 Equation 1

S = 4·15 -12

S = 60 - 12 = 48 → number of students

Answer: There are 48 students in the class.

Verification

There are 48 students and 15 benches.

If 4 students sit on each bench, 3 benches are left vacant.

48students ÷ 4students/bench = 12 benches are occupied and left 3 vacant benches.

If 3 students sit on each bench, 3 students still standing.

15benches * 3 students/bench = 45 students are sitting and 3 students remain standing.

Checked!!

$\textit{\textbf{Spymore}}$​​​​​​