College

Adam is creating an animated short film, and he needs 24 frames per second of film. He already has at least 250 frames. Which inequality represents this situation where [tex]f[/tex] is the number of frames and [tex]s[/tex] is the number of seconds of film?

A. [tex]s \geq 24f - 250[/tex]
B. [tex]f \geq 24s - 250[/tex]
C. [tex]f \geq 24s + 250[/tex]
D. [tex]9 \geq 24f + 250[/tex]

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]