Question

On the first day of the play the auditorium was 1/3 full, on the second day it was it was 5/12 full, and on the third day it was 1/2 full. if this pattern continues, how full will it be on the fourth day?

Answer 1

7/12.

If you make 1/3, 5/12, and 1/2 the same denominator, it will be:
4/12,5/12,and 6/12.

you can see that these fractions are increasing 1/12 for each day. so on the forth day, it will be 7/12.

Answer 2

`\bf\textbf{Part of auditorium filled on fourth day = }(7)/(12)`

Explanation:

`\text{Part of the auditorium filled on first day = }(1)/(3)\\\\\text{Part of the auditorium filled on second day = }(5)/(12)\\\\\text{Increase in the part of auditorium filled on second day than first day = }(5)/(12)-(1)/(3)\\\\=(5-4)/(12)\\\\=(1)/(12)`

`\text{Part of the auditorium filled on third day = }(1)/(2)\\\\\text{Increase in the part of auditorium filled on third day than second day = }(1)/(2)-(5)/(12)\\\\=(6-5)/(12)\\\\=(1)/(12)`

`\text{Hence, each day the auditorium is filled }(1)/(12)\text{ part more}\\\\\bf\textbf{So, Part of auditorium filled on fourth day = }(1)/(2)+(1)/(12)\\\\(6+1)/(12)\\\\=(7)/(12)`