Web Music Store Offers Two Versions Of A Popular Song

A Web Music Store Offers Two Versions Of A Popular Song The Size Of T

A web music store offers two versions of a popular song. The size of the standard version is 2.1 megabytes (MB), and the size of the high-quality version is 4.5 MB. Yesterday, the high-quality version was downloaded twice as often as the standard version. The total size downloaded for both versions was 2553 MB. How many downloads of the standard version were there?

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The problem involves determining the number of downloads for two versions of a song based on given data about their sizes, download ratios, and total downloaded data. To solve this, we set up algebraic equations representing the scenario.

Let the number of standard version downloads be \( x \). Since the high-quality version was downloaded twice as often as the standard version, the number of high-quality version downloads is \( 2x \). The sizes of the two versions are given as 2.1 MB for the standard and 4.5 MB for the high-quality version.

The total amount of data downloaded is the sum of the sizes of all downloaded standard and high-quality versions. Therefore, the total download size in MB can be expressed as:

\( 2.1x + 4.5(2x) = 2553 \)

Simplifying this equation:

\( 2.1x + 9x = 2553 \)

\( 11.1x = 2553 \)

Dividing both sides by 11.1 gives:

\( x = \frac{2553}{11.1} \)

Calculating this division:

\( x \approx 229.73 \)

Since the number of downloads should be a whole number, and considering the context of the problem, the closest integer is approximately 230 downloads of the standard version.

To verify, we calculate the total download in MB with \( x = 230 \):

Standard version: \( 2.1 \times 230 = 483 \) MB

High-quality version: \( 2 \times 230 = 460 \) downloads, total MB: \( 4.5 \times 460 = 2070 \) MB

Total MB downloaded: \( 483 + 2070 = 2553 \) MB, which matches the given total.

Thus, the number of downloads of the standard version is approximately 230.

References

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