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?
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}.
Let's assume the number of downloads of the standard version is "x".
Since the high-quality version was downloaded twice as often as the standard version, the number of downloads for the high-quality version would be 2x.
The size of the standard version is 2.1 MB, so the total size downloaded for the standard version would be 2.1x MB.
The size of the high-quality version is 4.6 MB, so the total size downloaded for the high-quality version would be 4.6(2x) MB.
The total size downloaded for both versions is given as 2599 MB, so we can set up the equation:
2.1x + 4.6(2x) = 2599
Simplifying the equation:
2.1x + 9.2x = 2599
11.3x = 2599
Dividing both sides by 11.3:
x = 2599 / 11.3
x ≈ 229.37
Since we can't have a fraction of a download, we round this value to the nearest whole number:
x ≈ 229
Therefore, there were approximately 229 downloads of the standard version.
To solve this problem, we can set up a system of equations based on the given information:
Let's represent the number of downloads of the standard version as "S" and the number of downloads of the high-quality version as "H".
We know that the size of the standard version is 2.1 MB, so the size of all the standard version downloads combined is 2.1S MB.
We also know that the size of the high-quality version is 4.6 MB, and because it was downloaded twice as often as the standard version, the size of all the high-quality version downloads combined is 4.6H MB.
The total size downloaded for the two versions was 2599 MB, so we can set up the equation:
2.1S + 4.6H = 2599
We also have the information that the high-quality version was downloaded twice as often as the standard version, so we can set up another equation:
H = 2S
Now we can solve this system of equations to find the values of S and H.
Substituting the value of H from the second equation into the first equation, we get:
2.1S + 4.6(2S) = 2599
2.1S + 9.2S = 2599
11.3S = 2599
S = 229.91 (rounded to two decimal places)
Since we cannot have a fraction of a download, we need to round the value of S to the nearest whole number. Therefore, there were approximately 230 downloads of the standard version.