Answer:
You don't have enough money for 2 downloads
Step-by-step explanation:
The complete question is
The price for digital downloads of music is represented by the linear function f(x) shown on the graph. The price for digital downloads of movies is represented by g(x) = 3x, where x is the number of movies downloaded and g(x) is the total cost in dollars. Graph of a line with equation f of x equals one half times x plus 2. The x-axis is labeled Number of Songs, and the y-axis is labeled Price in Dollars. You want to make 2 downloads, and you have $2.50. Determine the least expensive option.
You download 2 songs.
You download 2 movies.
You download 1 song and 1 movie.
You don't have enough money for 2 downloads.
we have
[tex]f(x)=\frac{1}{2}x+2[/tex] ---> price for digital downloads of music
[tex]g(x)=3x[/tex] ---> price for digital downloads of movies
Verify all the options
case 1) You download 2 songs
Calculate f(2)
For x=2
[tex]f(2)=\frac{1}{2}(2)+2=\$3[/tex]
This option is not possible because
$3>$2.50 (don't have enough money)
case 2) You download 2 movies.
Calculate g(2)
For x=2
[tex]g(2)=3(2)=\$6[/tex]
This option is not possible because
$6>$2.50 (don't have enough money)
case 3) You download 1 song and 1 movie.
Calculate f(1) and g(1)
For x=1
[tex]f(1)=\frac{1}{2}(1)+2=\$2.5[/tex]
[tex]g(1)=3(1)=\$3[/tex]
so
[tex]f(1)+g(1)=\$2.5+\$3=\$5.5[/tex]
This option is not possible because
$5.5>$2.50 (don't have enough money)
case 4) You don't have enough money for 2 downloads
The statement is true
You have only enough money for download 1 song
