Answer :
To solve this problem, we need to understand the relationship between frames and seconds in the context of the animated short film Adam is creating.
Here's a breakdown of the situation:
1. Requirement for film: Adam needs 24 frames per second. This means for every second of film, there should be at least 24 frames.
2. Existing frames: Adam already has at least 250 frames. This is an initial count that Adam can use towards meeting his requirements for the film's duration.
Let's define:
- [tex]\( f \)[/tex] as the number of frames Adam currently has.
- [tex]\( s \)[/tex] as the number of seconds of film he wants to create.
From the problem:
- The total number of frames Adam needs for [tex]\( s \)[/tex] seconds of film is given by [tex]\( 24s \)[/tex] (since he needs 24 frames for every second).
- Since Adam already has at least 250 frames, the actual requirement for additional frames to meet [tex]\( 24s \)[/tex] need not be fully acquired because he starts with these 250 frames.
Thus, the inequality to represent this situation can be derived as follows:
[tex]\[ f \geq 24s - 250 \][/tex]
This inequality expresses that the number of frames [tex]\( f \)[/tex] already available (including additional ones) should be at least 250 frames added to the total requirement equivalent to [tex]\( 24 \)[/tex] frames per second.
Therefore, the correct inequality is:
[tex]\( f \geq 24s - 250 \)[/tex]
Here's a breakdown of the situation:
1. Requirement for film: Adam needs 24 frames per second. This means for every second of film, there should be at least 24 frames.
2. Existing frames: Adam already has at least 250 frames. This is an initial count that Adam can use towards meeting his requirements for the film's duration.
Let's define:
- [tex]\( f \)[/tex] as the number of frames Adam currently has.
- [tex]\( s \)[/tex] as the number of seconds of film he wants to create.
From the problem:
- The total number of frames Adam needs for [tex]\( s \)[/tex] seconds of film is given by [tex]\( 24s \)[/tex] (since he needs 24 frames for every second).
- Since Adam already has at least 250 frames, the actual requirement for additional frames to meet [tex]\( 24s \)[/tex] need not be fully acquired because he starts with these 250 frames.
Thus, the inequality to represent this situation can be derived as follows:
[tex]\[ f \geq 24s - 250 \][/tex]
This inequality expresses that the number of frames [tex]\( f \)[/tex] already available (including additional ones) should be at least 250 frames added to the total requirement equivalent to [tex]\( 24 \)[/tex] frames per second.
Therefore, the correct inequality is:
[tex]\( f \geq 24s - 250 \)[/tex]
