Question

9. For a function, the chairs for seating were arranged in such a way that the number of rows and columns were the same. If there were 3100 chairs, how many more chairs are needed for such an arrangement? How many rows are there ..

​

Answer 1

Answer:

36 number of chairs required..

Explanation:

Let N denotes the required equal number of rows and columns.

Hence from above data we get following relation,

N^2 = 3100

or N = √3100 = 55.68 ≈ 56 [next higher integer]

Therefore it is evident from above that

for an arrangement of equal number of rows and columns,

required number of more chairs = 56*56 - 3100 = 3136 - 3100 = 36 [Ans]

Answer 2

Answer:

★You will get 27 chairs-each row and 36 more chairs needed explanation is below↓

★This is explanation of how we got 27 chairs-each row;

→The number of chairs will need to be a multiple of 27 (so they can have “m” rows of 27 chairs each, for a total of 27m chairs) and also a multiple of 33 (so they can have “n” rows of 33 chairs each, for a total of 33n chairs).

→What is the least common multiple (LCM) of 27 and 33?

→If you set 27m equal to the LCM, what value do you get for “m”? (This is the number of 27-chairs-each rows you can get.)

→If you get 33n equal to the LCM, what value do you get for “n”? (This is the number of 33-chairs-each rows you can get.)

{Note: This is only the SMALLEST number of chairs for which you can set up the chairs in the stipulated manner. Any multiple of the LCM will work, also}.

★Explanation of how we got 36 chairs;

≈First we need to take square root of 3100

≈ We will get 55 as quotient and 75 as remainder..

→Find √55

its 3025

≈56 is the next perfect square number

→Find it's square

≈its 3136

then subtract 3100 from 3136

we will get 36

Hence, 36 more chairs needed.

hope it's helpful to you!