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 690 downloads of the song, for a total download size of 2829 MB. How many downloads of the high-quality version were there?

Answer 1

Answer: 460 high-quality downloads

Given that the number of downloads were 690, we can make a statement:

Let S be "standard", and Let H be "high-quality"

S + H = 690

Then, since the total download size was 2829MB, we can make another statement:

2.7S + 4.8H = 2829

We now have two Equations:

Equation 1: S + H = 690

Equation 2: 2.7S + 4.8H = 2829

Now, since we are asked to find the number of high-quality downloads (H), we will rewrite the first equation in terms of S, and then solve for H through substitution.

Equation 1: S + H = 690

Equation 3: S = 690 - H

We will substitute the value of S into the second equation.

`2.7S+4.8H=2829`
`2.7(690-H)+4.8H=2829`
`1863-2.7H+4.8H=2829`
`-2.7H+4.8H=2829-1863`
`2.1H=966`
`H=(966)/(2.1)=460`

There are a total of 460 high-quality downloads.