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 4.4 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 5427 MB. How many downloads of the standard version were there?

Answer 1

270 downloads

Explanation:

Call x the number of times the standard quality version was downloaded and call y the number of times the high quality version was downloaded.

So, we know that

`2.5x + 4.4y = 5427` MB (1)

We also know that the high-quality version was downloaded four times as often as the standard version.

So

`y = 4x` (2)

We substitute equation (2) in equation (1) and solve for x.

`2.5x + 4.4 (4x) = 5427\\\\2.5x +17.6x = 5427\\\\20.1x=5427\\`

`x = 270\ downloads`