Question

). In a classroom there are a number of benches.
If 4 students sit on each bench, five benches
are left vacant; and if 3 students sit of each
bench, 4 students are left standing. Find the
number of benches and students in the
classroom​

Answer 1

Answer:

The number of benches are 24

The number of students are 76

Step-by-step explanation:

Given :

• If 4 students sit on each bench, five benches are left vacant and
• If 3 students sit of each bench, 4 students are left standing.

To find :

the number of benches and students in the classroom

Solution :

Let the number of benches be 'x' and the number of students be 'y'

According to the question :

First condition :-

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

The number of students = y

y = 4x – (4 × 5)

y = 4x – 20 —(1)

Second condition :-

If 3 students sit of each bench, 4 students are left standing.

y = 3x + 4 —(2)

From equations (1) and (2),

4x – 20 = 3x + 4

4x – 3x = 20 + 4

x = 24

Therefore, the number of benches are 24

Substitute in equation (2),

y = 3x + 4

y = 3(24) + 4

y = 72 + 4

y = 76

Therefore, the number of students are 76

Answer 2

Step-by-step explanation:

$\underline{\underline{\maltese\: \: \textbf{\textsf{Question}}}}$

• In a classroom there are a number of benches.If 4 students sit on each bench, five benches are left vacant; and if 3 students sit of each bench, 4 students are left standing. Find the number of benches and students in the classroom.

$\underline{\underline{\maltese\: \: \textbf{\textsf{Answer}}}}$

• Number of benches = 24.
• Number of students = 76.

$\underline{\underline{\maltese\: \: \textbf{\textsf{Given}}}}$

• If 4 students sit on each bench, five benches are left vacant and,
• If 3 students sit of each bench, 4 students are left standing.

$\underline{\underline{\maltese\: \: \textbf{\textsf{To\ Find}}}}$

• We have to find out the number of students and benches in the classroom.

$\underline{\underline{\maltese\: \: \textbf{\textsf{Solution}}}}$

• As per the given data, we know that 4 students sit on each bench, five benches are left vacant; and 3 students sit of each bench, 4 students are left standing.
• Then firstly, we will take the number of benches as 'x' and the number of students as 'y'.
• So, by using this required information we will create equations according to the given conditions and find the number of benches and students in the classroom.

$\underline{\underline{\maltese\: \: \textbf{\textsf{Calculations}}}}$

• If 4 students sit on each bench, five benches are left vacant.
• According to this condition we will create equation (1).

$\sf \mapsto {Number\ of\ students\ =\ y}$

$\sf \mapsto {y\ =\ 4x\ -\ (4 \times 5)}$

$\sf \mapsto {y\ =\ 4x\ -\ 20}$

${\therefore{\underline{\boxed{\tt {1^{st}\ equation,\ y\ =\ 4x\ -\ 20.}}}}}$

• If 3 students sit of each bench, 4 students are left standing.
• According to this condition, our required second equation is, y = 3x + 4.
• Now we have equation (1) and (2).
• So, from equation (1) and (2) we will find out the number of benches.

$\bf {\underline{\bigstar\ From\ equation\ (1)\ and\ (2)\ :-}}$

$\sf \mapsto {4x\ -\ 20\ =\ 3x\ +\ 4}$

$\sf \mapsto {4x\ -\ 3x\ =\ 20\ +\ 4}$

$\sf \mapsto {x\ =\ 24}$

${\therefore{\underline{\boxed{\tt {Number\ of\ benches\ =\ 24.}}}}}$

• Now we have the number of benches in classroom.
• So, by applying the value of number of benches in equation (2), we will get the number of students in classroom.

$\bf {\underline{\bigstar\ By\ substituting\ x\ =\ 24\ in\ equation\ (2)\ :-}}$

$\sf \mapsto {y\ =\ 3x\ +\ 4}$

$\sf \mapsto {y\ =\ 3(24)\ +\ 4}$

$\sf \mapsto {y\ =\ 72\ +\ 4}$

$\sf \mapsto {y\ =\ 76}$

${\therefore{\underline{\boxed{\tt {Number\ of\ students\ =\ 76.}}}}}$