Question

A Web music store offers two versions of a popular song. The size of the standard version is 2.5 megabytes (MB). The size of the high-quality version is 4.7 MB. Yesterday, there were 780 downloads of the song, for a total download size of 3006 MB. How many downloads of the standard version were there?

Answer 1

There were 300 standard version of songs downloaded at Web music store.

Explanation:

Let the number of standard version of song download be 'x'.

Let the number of high-quality version of song download be 'y'.

Given:

Total songs downloaded = 780

Now we know that;

Total songs downloaded is equal to sum of the number of standard version of song download and the number of high-quality version of song download.

framing in equation form we get;

`x+y=780\ \ \ \ \ equation \ 1`

Also Given:

Size of standard version of song = 2.5 MB

Size of high-quality version of song = 4.7 MB

Total Download size = 3006 MB

Now we know that;

Total Download size is equal to sum of Size of standard version of song multiplied by the number of standard version of song download and Size of high-quality version of song multiplied by the number of high-quality version of song download.

framing in equation form we get;

`2.5x+4.7y =3006 \ \ \ \ equation \ 2`

Now Multiplying equation 1 by 2.5 we get;

`2.5(x+y)=780* 2.5\\\\2.5x+2.5y = 1950 \ \ \ \ equation \ 3`

Now Subtracting equation 3 from equation 2 we get;

`(2.5x+4.7y)-(2.5x+2.5y) =3006 - 1950\\\\2.5x+4.7y-2.5x-2.5y = 1056\\\\2.2y =1056\\\\y =(1056)/(2.2)=480`

Substituting the value of y in equation 1 we get;

`x+y=780\\\\x+480=780\\\\x=780-480 = 300`

Hence there were 300 standard version of songs downloaded at Web music store.