A Web music store offers two versions of a popular song. The size of the standard version is 2.2 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 2850 MB. How many downloads of the standard version were there?
Let's call the number of downloads for the standard version "x".
According to the problem, the high-quality version was downloaded twice as often as the standard version. So the number of downloads for the high-quality version would be 2x.
We also know that the total size downloaded for the two versions was 2850 MB. So the total size of the standard version downloaded would be 2.2x (since the size of each download is 2.2 MB), and the total size of the high-quality version downloaded would be 4.6(2x) = 9.2x (since the size of each download is 4.6 MB and there were 2x downloads).
Now we can set up an equation:
2.2x + 9.2x = 2850
Simplifying:
11.4x = 2850
Dividing both sides by 11.4:
x = 250
So there were 250 downloads of the standard version.
To check, we can find the number of downloads of the high-quality version:
2x = 2(250) = 500
And we can confirm that the total size downloaded for both versions is 2850 MB:
2.2(250) + 4.6(500) = 550 + 2300 = 2850
Thus, our answer is correct.
Let's assume the number of downloads of the standard version is X.
According to the given information, the size of the standard version is 2.2 MB and the size of the high-quality version is 4.6 MB.
So, the size of the high-quality version downloaded would be 2 * X * 4.6 MB, as it was downloaded twice as often as the standard version.
The total size downloaded for the two versions is given as 2850 MB. Therefore, we can write the equation:
2.2 X + 2 * X * 4.6 = 2850
Now, let's solve this equation to find the value of X:
2.2 X + 9.2 X = 2850
11.4 X = 2850
Dividing both sides by 11.4:
X = 2850 / 11.4
X = 250
Therefore, there were 250 downloads of the standard version.