You have 60 megabytes of space left on your portaable media player. You can choose to download song files that use 3.5 megabytes or video files that use 8 megabytes. You want to download at least 12 files. What is a graph showing the numbers of songs and video files you can download?
x + y >= 12 files
3.5x + 8y <= 60 MB
--> 3.5x + 8 (12-x) <= 60
3.5x - 8x + 96 <= 60
96 - 60 <= 4.5x
=> x = 36/4.5 = 8 songs
Thus y = 12 - 8 = 4 videos
To create a graph showing the number of songs and video files you can download, we can use a coordinate system where the x-axis represents the number of songs and the y-axis represents the number of video files.
Let's calculate the maximum number of songs and video files you can download with the given 60 megabytes of space.
For songs:
Each song file uses 3.5 megabytes.
Total megabytes for songs = 60 megabytes
Maximum songs = Total megabytes for songs / File size per song = 60 megabytes / 3.5 megabytes
For videos:
Each video file uses 8 megabytes.
Total megabytes for videos = 60 megabytes
Maximum videos = Total megabytes for videos / File size per video = 60 megabytes / 8 megabytes
Now, we can generate a table or a graph to visualize this:
Number of Songs Number of Videos
0 7 (Maximum videos)
1 6
2 5
3 4
4 3
5 2
6 1
7 0
This graph represents the number of songs and video files you can download on your portable media player, given the file sizes and the available 60 megabytes of space.
To create a graph showing the numbers of songs and video files you can download, we can use the x and y-axis to represent the number of songs and video files, respectively. We will use the given file sizes to determine the limitations on the number of files that can be downloaded.
Let's start by calculating the maximum number of songs and video files that can be downloaded with the available space of 60 megabytes:
Maximum number of songs = (Available space) / (File size of each song)
= 60 megabytes / 3.5 megabytes ≈ 17.14 songs
Maximum number of video files = (Available space) / (File size of each video)
= 60 megabytes / 8 megabytes ≈ 7.5 video files
Since you want to download at least 12 files, we need to find a combination of songs and video files that add up to at least 12.
One way to graphically represent these combinations is to plot all possible values within the given constraints. Let's create a table showing the number of songs and video files that can be downloaded:
Number of Songs | Number of Video Files
-------------------------------------
0 | 7
1 | 6
2 | 5
3 | 4
4 | 3
5 | 2
6 | 1
7 | 0
By plotting these values on a graph with the x-axis representing the number of songs and the y-axis representing the number of video files, we will have a visual representation of the available combinations.