Ari watched 1 4 of a movie in the morning, and she watched some more at night. By the end of the day, she still had 1 3 of the movie left to watch. How much of the movie did Ari watch at night?

Answer: Ari watched 5/12 of the movie at night.

Step-by-step explanation:

Let x represent the portion of the movie that Ari watched at night.

Ari watched 1 4 of a movie in the morning, and she watched some more at night. It means that the total portion she has watched already is 1/4 + x

The portion of the movie remaining for her to watch is

1 - (1/4 + x) = 1 - (1 + 4x) / 4

By the end of the day, she still had 1 3 of the movie left to watch. It means that

1/3 = 1 - (1 + 4x) / 4

1/3 = (4 - 1 - 4x) / 4

1/3 = (3 - 4x) / 4

Cross multiplying by 3, it becomes

1 = 3 (3 - 4x) / 4

Multiplying through by 4, it becomes

4 = 3 (3 - 4x)

4 = 9 - 12x

12x = 9 - 4

12x = 5

x = 5/12