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

Answer:

$\bf\textbf{Part of auditorium filled on fourth day = }\frac{7}{12}$

Step-by-step explanation:

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

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

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