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There are some benches in the classroom. If 4 students sit on each bench, then 4 benches are left unoccupied, However, if 3 students sit on each bench, then 3 students are left standing. Then the sum of the number of benches and the number of students in that classroom is

There are some benches in the classroom. If 4 students sit on each bench, then 4 benches are left unoccupied, However, if 3 students sit on each bench, then 3 students are left standing. Then the sum of the number of benches and the number of students in that classroom is Correct Answer 79

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

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

Now according to the given statements,

If 4 students sit on each bench, then 4 benches are left unoccupied,

∴ y = 4x - (4 × 4) 

∴ y = 4x - 16 ..............(1)

and if 3 students sit on each bench, then 3 students are left standing,

∴ y = 3x + 3 ..................(2)

From eq. 1 and 2, we get,

4x - 16 = 3x + 3

∴ 4x - 3x = 3 + 16

∴ x = 19

By substituting value of 'x' in the eq. (1), we get,

y = 4(19) - 16

∴ y = 76 - 16

∴ y = 60

Hence, the total number of students in the class are 60, 

and the total number of benches in the class are 19.

Hence, the sum of the number of students and benches are,

60 + 19 = 79

Hence, 79 is the correct answer.

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