Question

A Web music store offers two versions of a popular song. The size of the standard version is 2.1 megabytes (MB). The size of the high-quality version is

4.4 MB. Yesterday, there were 1310 downloads of the song, for a total download size of 4752 MB. How many downloads of the standard version were there?

Answer 1

There were 440 Standard version of songs downloaded in Web music store.

Explanation:

Given,

Total number of songs downloaded = 1310

Total size of the downloaded songs = 4752 MB

Size of standard version of song = 2.1 MB

Size of high quality version of song = 4.4 MB

Solution,

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

And also let the number of high quality version of song be 'y'.

Now, total number of songs is the sum of total number of standard version of song and total number of high quality version of song.

On framing the above sentence in equation form, we get;

`x+y=1310\ \ \ \ \ equation\ 1`

Now, Total size of the downloaded songs is the sum of total number of standard version of song multiplied with size of standard version of song and total number of high quality version of song multiplied with size of high quality version of song.

On framing the above sentence in equation form, we get;

`2.1x+4.4y=4752`

Multiplying with 10 on both side, we get;

`10(2.1x+4.4y)=4752*10\\\\21x+44y=47520\ \ \ \ equation\ 2`

Now multiplying equation 1 by 21, we get;

`21(x+y)=1310*21`\\\\21x+21y=27510\ \ \ \ equation\ 3`

Now subtract equation 3 from equation 2, we get;

`(21x+44y)-(21x+21y)=47520-27510\\\\21x+44y-21x-21y=20010\\\\23y=20010\\\\y=(20010)/(23)\\\\y=870`

On substituting the value of y in equation 1, we get the value of x;

`x+y=1310\\\\x+870=1310\\\\x=1310-870=440`

Hence There were 440 Standard version of songs downloaded in Web music store.