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Jackson has 50 megabytes (MB) of space left on his smartphone. He can download songs that each use 3.5 MB or videos that each use 7 MB. He wants to download at least 10 new media files.

Which pair of inequalities specifies the number of song files, [tex]\(x\)[/tex], and the number of video files, [tex]\(y\)[/tex], that Jackson can download?

A. [tex]\(3.5x + 7y \leq 50\)[/tex]
[tex]\[x + y \geq 10\][/tex]

B. [tex]\(3.5x + 7y \ \textgreater \ 50\)[/tex]
[tex]\[x + y \geq 10\][/tex]

C. [tex]\(3.5x + 7y \leq 50\)[/tex]
[tex]\[x + y \ \textgreater \ 10\][/tex]

D. [tex]\(3.5x + 7y \geq 10\)[/tex]
[tex]\[x + y \leq 50\][/tex]



Answer :

GinnyAnswer
To help Jackson determine how many songs and videos he can download, we need to establish two inequalities based on the conditions given in the problem.

### Conditions Given:
1. Jackson has 50 MB of space on his smartphone.
2. Each song uses 3.5 MB of space.
3. Each video uses 7 MB of space.
4. Jackson wants to download at least 10 media files in total.

### Formulating the Inequalities:

1. Space Constraint:
The total space consumed by the media files (songs and videos) must not exceed 50 MB. If [tex]\(x\)[/tex] represents the number of songs and [tex]\(y\)[/tex] represents the number of videos:
[tex]\[ 3.5x + 7y \leq 50 \][/tex]

2. Minimum Number of Files Constraint:
The total number of media files must be at least 10.
[tex]\[ x + y \geq 10 \][/tex]

Therefore, the pair of inequalities that specify the number of song files [tex]\(x\)[/tex] and video files [tex]\(y\)[/tex] that Jackson can download is:

[tex]\[ \begin{aligned} 3.5x + 7y & \leq 50 \\ x + y & \geq 10 \end{aligned} \][/tex]

### Answer:
The correct choice is:
A.
[tex]\[ \begin{aligned} 3.5x + 7y & \leq 50 \\ x + y & \geq 10 \end{aligned} \][/tex]

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