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Students of a class are made to stand in rows. If 4 students are extra in a row, there would be 2 rows less .If 4 students are less in a row , there would be 4 more rows . Find the number of students in the class .?
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Problem Statement
Students of a class are made to stand in rows. If 4 students are extra in a row, there would be 2 rows less .If 4 students are less in a row , there would be 4 more rows . Find the number of students in the class.
Step-by-Step Solution
- Let's assume there are n students in the class.
- Let's assume there are m rows in the class.
- From the given information, we can write two equations:
- n = (m+2)(x-4) where x is the number of students in each row when there are 4 extra students in each row.
- n = (m-4)(x+4) where x is the number of students in each row when there are 4 fewer students in each row.
- Expanding the equations, we get:
- nx - 4m = mx - 8 + 2x - 8
- nx + 4m = mx + 16 + 4x + 16
- Simplifying the equations, we get:
- (n-2x+16)/4 = m
- (n+4x+32)/4 = m
- Equating the two equations, we get:
- n-2x+16 = n+4x+32
- Simplifying the equation, we get:
- 6x = n-16
- Substituting this value of 6x in the two equations we derived earlier, we get:
- n = 6m + 56
- n = 6m - 8
- Equating the two equations, we get:
- 6m + 56 = 6m - 8
- This equation has no solution, which means our initial assumption was incorrect.
- Let's assume there are n students in the class and x students in each row.
- From the given information, we can write two equations:
- n = (m+2)(x-4) where m is the number of rows when there are 4 extra students in each row.
- n = (m-4)(x+4) where m is the number of rows when there are 4 fewer students in each row.
- Expanding the equations, we get:
- nx - 4m
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Students of a class are made to stand in rows. If 4 students are extra in a row, there would be 2 rows less .If 4 students are less in a row , there would be 4 more rows . Find the number of students in the class .?
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