Question

The price for digital downloads of music is represented by the linear functions 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.

Answer 1

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

$f(x)=\frac{1}{2}x+2$ ---> price for digital downloads of music

$g(x)=3x$ ---> price for digital downloads of movies

Verify all the options

case 1) You download 2 songs

Calculate f(2)

For x=2

$f(2)=\frac{1}{2}(2)+2=\ 3$

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

$g(2)=3(2)=\ 6$

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

$f(1)=\frac{1}{2}(1)+2=\ 2.5$

$g(1)=3(1)=\ 3$

so

$f(1)+g(1)=\ 2.5+\ 3=\ 5.5$

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