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 4.6 MB. Yesterday, the high-quality version was downloaded twice as often as the standard version. The total size downloaded for the two versions was 2599 MB. How many downloads of the standard version were there?

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 4.6 MB. Yesterday, the high-quality version was downloaded twice as often as the standard version. The total size downloaded for the two versions was 2599 MB. How many downloads of the standard version were there?

GPT 3.5 · Answer

Let x be the number of downloads of the standard version.
The number of downloads of the high-quality version is 2x.
The total size downloaded for the standard version is 2.1 * x MB.
The total size downloaded for the high-quality version is 4.6 * 2x = 9.2x MB.
The total size downloaded for both versions is 2.1 * x + 9.2x = 2599 MB.
Combining like terms, we get 11.3x = 2599.
Dividing both sides by 11.3, we get x = 229.
Therefore, there were 229 downloads of the standard version. Answer: \boxed{229}.