Question

In a school auditorium, the number of chairs in a row is the same as the number of rows of chairs. There are 7033 students in the school. If we know that less than 31 chairs were empty, how many chairs were empty after all the students sat down?

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Solution

Let chairs in row be x

so number of rows also , x

total number of chairs = x * x

= x^2

there are 7033 students in school and each student gets chair . some chairs leaves empty

so , x^2 > 7033 , such that x^2 is not exceeds than 7033 + 31 = 7064

so finding the square number just below 7064

80^2 = 6400

90^2 = 8100

the number is between 80 and 90

now 85^2 = 7225

so expected number is below 85

83^2 = 688984^2 = 7056

so x^2 = 7056 = 84^2

which is total number of chairs in auditorium

so 7056 - 7033 = 23

23 chairs remains empty.

so number of rows also , x

total number of chairs = x * x

= x^2

there are 7033 students in school and each student gets chair . some chairs leaves empty

so , x^2 > 7033 , such that x^2 is not exceeds than 7033 + 31 = 7064

so finding the square number just below 7064

80^2 = 6400

90^2 = 8100

the number is between 80 and 90

now 85^2 = 7225

so expected number is below 85

83^2 = 688984^2 = 7056

so x^2 = 7056 = 84^2

which is total number of chairs in auditorium

so 7056 - 7033 = 23

23 chairs remains empty.

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