Questions: A Web music store offers two versions of a popular song. The size of the standard version is 2.4 megabytes (MB). The size of the high-quality version is 4.6 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 5616 MB. How many downloads of the standard version were there? Number of standard version downloads:

A Web music store offers two versions of a popular song. The size of the standard version is 2.4 megabytes (MB). The size of the high-quality version is 4.6 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 5616 MB. How many downloads of the standard version were there?

Number of standard version downloads:

Transcript text: A Web music store offers two versions of a popular song. The size of the standard version is 2.4 megabytes (MB). The size of the high-quality version is 4.6 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 5616 MB. How many downloads of the standard version were there? Number of standard version downloads: $\square$

Solution

Solution Steps

Step 1: Define Variables

Let $ s $ represent the number of downloads of the standard version, and $ h $ represent the number of downloads of the high-quality version.

Step 2: Set Up Equations

From the problem statement, we have two key pieces of information:

The high-quality version was downloaded four times as often as the standard version: \[ h = 4s \]
The total size of all downloads was 5616 MB: \[ 2.4s + 4.6h = 5616 \]

Step 3: Substitute and Solve

Substitute the expression for $ h $ from the first equation into the second equation: \[ 2.4s + 4.6(4s) = 5616 \] Simplify and solve for $ s $: \[ 2.4s + 18.4s = 5616 \] \[ 20.8s = 5616 \] \[ s = \frac{5616}{20.8} = 270 \]