Question

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, x, and the number of video files, y, that Jackson can download

Answer 1

`3.5x+7y\leq 50`

`x+y\geq 10`

Explanation:

Given : 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.

To find : The pair of inequalities specifies the number of song files, x, and the number of video files, y, that Jackson can download.

Solution :

The number of song files Jackson can download is x

The number of video files Jackson can download is y

→ x song files occupy a space of 3.5 MB per file,

So, number of space occupy by songs files = 3.5x MB

→ y media files occupy a space of 7 MB per file,

So, number of space occupy by video files = 7y MB

→ The total amount of MB used is
`3.5x+7y`

Jackson has 50 megabytes (MB) of space left on his smartphone.

The total amount must be less than or equal to 50 MB,

which can be represented as
`3.5x+7y\leq 50`

Jackson wants to download at least 10 media files,

which means
`x+y\geq 10`

Therefore, The two inequality form is

`3.5x+7y\leq 50`

`x+y\geq 10`

Answer 2

The number of song files Jackson can download: x

The number of video files Jackson can download: y



x song files occupy a space of 3.5MB per file, times x files = 3.5x MB

y media files occupy a space of 7MB per file, times y files = 7yMB


(3.5x + 7y) MB must be at most 50 MB, since there is 50 MB left,

this can be represented by the inequality:
`i) \ \ 3.5x+7y \leq 50`


Jackson wants to download at least 10 media files, so y must be at least 10

this means that
`ii) \ \ \ y \geq 10`


Answer:
`i) \ \ 3.5x+7y \leq 50\\\\ii) \ \ \ y \geq 10`