At a particular movie, what was the ratio of the number of people who

At a particular movie, what was the ratio of the number of people who watched the entire movie to the number of people who left the movie before it ended? (Assume all audience members were in their seats by the start of the movie.

(1) At the beginning of the movie, with the entire audience seated, the ratio of the number of seats filled to the number of seats not filled was 5 to 6.
(2) At the end of the movie, the ratio of the number of seats filled to seats not filled was 1 to 3.
Can anyone tell me the correct answer?

With ratios, it's useful to pick numbers. In this example, it is clear that each statement by itself is not sufficient, so let's take them together.

1) Ratio of filled to unfilled is 5:6. This means the number of total seats is a multiple of 11.

2) Ratio of filled to unfilled is 1:3. This means the number of total seats is also a multiple of 4.

Let's then pick a number for the total number of seats that is a multiple of 11 and 4: 44.

With this number, we now have the following ratios:

1) 20:24 (we multiplied everything by 4 to have a total of 44)
2) 11:33 (we multiplied everything by 11 to have a total of 44)

This means that we had 20 people in the beginning and only 11 in the end, which means that 9 people left. It makes sense: we had 24 unfilled in the beginning and 24+9=33 unfilled in the end, from the 9 that left.

The question asks the ratio of people who watched the entire movie to people who didn't, or 11/9.

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