A Web music store offers two versions of a popular song The

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 4.2 MB. Yesterday, there were 1480 downloads of the song, for a total download size of 5128 MB. How many downloads of the high-quality version were there?

Solution

Let, there be X downloads of the high-quality version.

Then, there were (1480 - X) downloads of the standard version.

Given that the sizes of the standard version and high-quality version of songs are 2.5 MB and 4.2 MB respectively.

Therefore, by given conditions,

(4.2 * X) + [2.5 * (1480 - X)] = 5128

i.e., (4.2 * X) + (2.5 * 1480) - (2.5 * X) = 5128

i.e., [(4.2 - 2.5) * X] + 3700 = 5128

i.e., 1.7 * X = 5128 - 3700

i.e., X = 1428 / 1.7

i.e., X = 840

Therefore, there were 840 downloads of the high-quality version.