Question

A teacher has enough sheets of papers to give each student of her class. When she gives each student 3 sheets she has 31 left with her, and when she gives 4 sheets to each student she has 8 left. How many students are there in her class?

Answer 1

Answer:

when she gives 3 sheets to each student 31 are left

when she gives 4 sheets 8 are left

31-8=23

there are 23 students in class

Answer 2

Number of students in the class = 23

Given :

• A teacher has enough sheets of papers to give each student of her class.

• When the teacher gives 3 sheets to each student she has 31 left with her

• When the teacher gives 4 sheets to each student she has 8 left

To find :

Number of students in the class

Solution :

Step 1 of 2 :

Form the equation to calculate number of students in the class

Let number of students in the class = n

When the teacher gives 3 sheets to each student she has 31 left with her

∴ Number of sheets = 3n + 31

When the teacher gives 4 sheets to each student she has 8 left

∴ Number of sheets = 4n + 8

By the given condition

$\displaystyle \sf 3n + 31 = 4n + 8$

Step 2 of 2 :

Calculate number of students in the class

$\displaystyle \sf 3n + 31 = 4n + 8$

$\displaystyle \sf{ \implies }3n - 4n = 8 - 31$

$\displaystyle \sf{ \implies } - n = - 23$

$\displaystyle \sf{ \implies } n = 23$

∴ Number of students in the class = n = 23

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