Question

A Web music store offers two versions of a popular song. The size of the standard version is 2.7 megabytes (MB). The size of the high-quality version is 4.8 MB. Yesterday, there were 1400 downloads of the song, for a total download size of 5523 MB. How many downloads of the standard version were there? Number of standard version downloads:

Answer 1

Given:

$\begin{gathered} Standard-version-size=2.7MB \\ High-quality-version-size=4.8MB \end{gathered}$

To Determine: The number of standard version downloads

Solution

Let the number of downloads for standard version be x and the number of downloads for high-quality version be y

Therefore

$\begin{gathered} x+y=1400===equation1 \\ 2.7x+4.8y=5523===equation2 \end{gathered}$

Combine the two equations together

$\begin{gathered} From\text{ equation 1} \\ y=1400-x \\ Substitute\text{ for y in equation 2} \\ 2.7x+4.8(1400-x)=5523 \\ 2.7x+6720-4.8x=5523 \\ 2.7x-4.8x=5523-6720 \\ -2.1x=-1197 \\ x=\frac{-1197}{-2.1} \\ x=570 \end{gathered}$

Substitute for x in equation 1

$\begin{gathered} 570+y=1400 \\ y=1400-570 \\ y=830 \end{gathered}$

Hence, the number of standard version downloads is 570