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]\( s \geq 24f + 250 \)[/tex]

C. [tex]\( f \geq 24s + 250 \)[/tex]

D. [tex]\( f \geq 24s - 250 \)[/tex]

Answer :

To solve this problem, we need to understand the relationship between frames and seconds in the context of Adam's film.

1. Understand the Context:
- Adam needs 24 frames per second for his animated film.
- He already has at least 250 frames.

2. Understand the Variables:
- Let [tex]\( f \)[/tex] be the number of frames.
- Let [tex]\( s \)[/tex] be the number of seconds of film that he can make.

3. Frames for Seconds:
- For each second of the film, 24 frames are needed, so [tex]\( f = 24 \times s \)[/tex].

4. Total Frames Requirement:
- Adam already has at least 250 frames. This means the total frames he has is at least [tex]\( 250 + 24 \times s \)[/tex] (since he continues to add more frames as per the requirement of the seconds).

5. Set Up the Inequality:
- Since he needs at least the frames required for the seconds plus the extra 250 he already has, the inequality that describes this situation would be:
[tex]\[
f \geq 24s - 250
\][/tex]

Thus, the correct inequality for this situation is [tex]\( f \geq 24s - 250 \)[/tex].