A Web music store offers two versions of a popular song. The size of the standard version is  2.6  megabytes (MB). The size of the high-quality version is  4.3 MB. Yesterday, the...

A Web music store offers two versions of a popular song. The size of the standard version is 

2.6

 megabytes (MB). The size of the high-quality version is 

4.3

MB. Yesterday, the high-quality version was downloaded four times as often as the standard version. The total size downloaded for the two versions was 

5346

 MB. How many downloads of the standard version were there? 

Asked on by enotes

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hkj1385's profile pic

hkj1385 | (Level 1) Assistant Educator

Posted on

Let the standard quality version downloaded be 'x'

Thus, total size of high quality version downloaded = 2.6*x

Thus, total size of high quality version = 5346 - 2.6x

Now, as per the question, the high quality version downloaded = 4*x

Thus, 4x*4.3 = 5346-2.6x

or, 17.2x = 5346-2.6x

or, 19.8x = 5346

or, x = 270 = number of standard quality downloads.

ishpiro's profile pic

ishpiro | College Teacher | (Level 1) Educator

Posted on

Let's denote the number of downloads of the standard version by x and the number of downloads of the high-quality version by y.

Since yesterday the high-quality version was downloaded four times as often,

y = 4x.

The total size of the download of the standard version would be the number of downloads times the size of each song: 2.6x. Similarly, the total size of the download of the high-quality version would be the number of downloads times the size: 4.3y. So, the total size downloaded for two versions is

2.6x + 4.3y = 5346.

These two equations can be solved together as a system. The expression for y in terms of x, y = 4x, can be substituted into the second equation:

2.6x + 4.3(4x) = 5346.

2.6x + 17.2x = 5346

19.8x = 5346

Divide both sides by 19.8 to get 5346:

`x = 5346/19.8 =270 `

The were 270 downloads of the standard version of the song.

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