Question

There are certain number of benches in a classroom. If four students sit on each bench then three benches
remain unoccupied. If, however, three students sit on each bench then three students remain standing in the
class. Find the number of students in the class.

​

Answer 1

Basic Concept :-

Formulation of Linear Equation from Word Problem.

1. Understand the problem.

• Understand all the words used in stating the problem.

• Understand what you are asked to find.

2. Translate the problem to an equation.

• Assign a variable (or variables) to represent the unknown.

• Clearly mentioned what the variable represents.

3. Carry out the plan and solve the problem.

$\large\underline{\sf{Solution-}}$

Let assume that number of students in the class be 'x'.

and

Let number of benches in the class be 'y'.

According to statement,

If 4 students sit on each bench, then 3 benches remain unoccupied.

It implies, y - 3 benches are occupied by 'x' students.

$\rm \longmapsto\:y - 3= \dfrac{x}{4}$

$\bf \implies\: \red{ \bf \: y= \dfrac{x}{4} + 3} - - - (1)$

According to statement again,

If 3 students sit on each bench then 3 students remain standing in the class.

It implies, y benches are occupied by x - 3 students.

$\bf\implies \red{ \bf \: \:y \: = \: \dfrac{x - 3}{3}} - - - (2)$

On equating equation (1) and equation (2), we get

$\rm :\longmapsto\:\dfrac{x}{4} + 3 = \dfrac{x - 3}{3}$

$\rm :\longmapsto\:\dfrac{x + 12}{4}= \dfrac{x - 3}{3}$

$\rm :\longmapsto\:3x + 36 = 4x - 12$

$\rm :\longmapsto\:36 + 12 = 4x - 3x$

$\bf\implies \:x \: = \: 48$

On substituting the value of x in equation (2), we get

$\rm :\longmapsto\:y = \dfrac{48 - 3}{3}$

$\rm :\longmapsto\:y = \dfrac{45}{3}$

$\bf\implies \:y \: = \: 15$

$\bf\implies \purple{ \bf \: \:Number \: of \: benches \: in \: class = 15}$