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Caissa can download a maximum of 1000 megabytes (MB) of songs or movies to her smartphone each month. The file size of each movie is
85MB, and the file size of each song is
4MB.
Write an inequality that represents the number of movies
(M) and songs
(S) that Caissa can download each month.

Caissa can download a maximum of $1000\,\text{MB}$ of songs or movies to her smartphone each month. The file size of each movie is $85\,\text{MB}$ , and the file size of each song is $4\,\text{MB}$ . Write an inequality that represents the number of movies $(M)$ and songs $(S)$ that Caissa can download each month.

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Modeling with linear inequalities

Full solution

Q. Caissa can download a maximum of

1000\,\text{MB}

of songs or movies to her smartphone each month. The file size of each movie is

85\,\text{MB}

, and the file size of each song is

4\,\text{MB}

. Write an inequality that represents the number of movies

(M)

and songs

(S)

that Caissa can download each month.

Identify variables and file sizes: Identify the variables and their corresponding file sizes. $\newline$ Movies are represented by $M$ and each movie is $85\,\text{MB}$ . Songs are represented by $S$ and each song is $4\,\text{MB}$ . Caissa can download a maximum of $1000\,\text{MB}$ each month.
Write inequality for total file size: Write an inequality that represents the total file size of movies and songs downloaded. $\newline$ The total file size for movies downloaded is $85M$ and for songs is $4S$ . The sum of these must be less than or equal to $1000\,\text{MB}$ . $\newline$ So, the inequality is $85M + 4S \leq 1000$ .
Check if inequality makes sense: Check the inequality to ensure it makes sense in the context of the problem. $\newline$ If $M$ is $0$ (no movies downloaded), then $S$ can be at most $250$ (since $4 \times 250 = 1000$ ). If $S$ is $0$ (no songs downloaded), then $M$ can be at most $11$ (since $85 \times 11 = 935$ , and $0$ $0$ , which is greater than $0$ $1$ ). The inequality seems to correctly represent the situation.

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