Question

You have 60 megabytes (MB) of space left on your mp3. You can choose to download song files that use 3.5 MB or video files that use 8 MB. You want to download at least 12 files. What is a graph showing the numbers of song and video files you can download?

Answer 1

See below for an idea of how to construct a graph:

Explanation:

We want at least 12 files.

This means that we can have some idea as to the numbers of song and video files we can have. For instance, if we download no video files, we can download a maximum of `60/3.5=>17` song files. And so with no video files, we can have anywhere between 12 and 17 files.

If we put on the maximum number of video files, we end up with `60/8 =>` less than 12.

And so let's build a table of the maximum and minimum numbers of song files for a given number of video files:

`(("Videos","Songs max", "Songs min"),(0,17,12),(1,14,11),(2,13,10),(3,10,9),(4,8,8))`

We can set the "Videos" to be one axis (let's make it the `x` for this) and the "Songs" to the other (and so the `y` here). This gives the graph to be the points `(0,17), (0,16),(0,15)...(1, 14), (1,13)...(4,8)` or 17 points in total.