Write an inequality that represents the number of movies (M) and songs (S) that Caissa can download each month.
Understand the Problem
The question is asking for an inequality that represents the maximum number of movies (M) and songs (S) Caissa can download without exceeding a total of 1000 megabytes. Each movie is 85 MB and each song is 4 MB.
Answer
$$ 85M + 4S \leq 1000 $$
Answer for screen readers
The inequality that represents the number of movies ( M ) and songs ( S ) that Caissa can download is:
$$ 85M + 4S \leq 1000 $$
Steps to Solve
- Identify the variables
Let ( M ) represent the number of movies and ( S ) represent the number of songs.
- Determine the space taken by movies and songs
Each movie takes up 85 MB. So, the total space used by ( M ) movies is given by ( 85M ).
Each song takes up 4 MB. Therefore, the total space used by ( S ) songs is given by ( 4S ).
- Set up the inequality
Since the total download limit is 1000 MB, we can combine the space used by movies and songs:
[ 85M + 4S \leq 1000 ]
This represents the maximum number of movies and songs Caissa can download without exceeding 1000 MB.
The inequality that represents the number of movies ( M ) and songs ( S ) that Caissa can download is:
$$ 85M + 4S \leq 1000 $$
More Information
This inequality allows Caissa to assess her downloading options, considering both movies and songs, without exceeding her monthly storage limit. It can be used for determining combinations of movies and songs that fit her needs.
Tips
- Failing to include the inequality sign (≤), which is essential to indicate that the total size cannot exceed 1000 MB.
- Confusing the size of movies and songs when forming the inequality. Ensure that the correct figures (85 MB for movies and 4 MB for songs) are used.
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