A Web music store offers two versions of a popular song. The size of the standard version is
megabytes (MB). The size of the high-quality version is
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
MB. How many downloads of the standard version were there?
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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.
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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