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Problem PageQuestion A Web music store offers two versions of a popular song. The size of the standard version is 2.6 megabytes (MB). The size of the high-quality version is 4.2 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 4074 MB. How many downloads of the standard version were there?

Respuesta :

Answer:

There were 210 downloads of the standard version.

Step-by-step explanation:

This question can be solved using a system of equations.

I am going to say that:

x is the number of downloads of the standard version.

y is the number of downloads of the high-quality version.

The size of the standard version is 2.6 megabytes (MB). The size of the high-quality version is 4.2 MB. The total size downloaded for the two versions was 4074 MB.

This means that:

[tex]2.6x + 4.2y = 4074[/tex]

Yesterday, the high-quality version was downloaded four times as often as the standard version.

This means that [tex]y = 4x[/tex]

How many downloads of the standard version were there?

This is x.

[tex]2.6x + 4.2y = 4074[/tex]

Since [tex]y = 4x[/tex]

[tex]2.6x + 4.2*4x = 4074[/tex]

[tex]19.4x = 4074[/tex]

[tex]x = \frac{4074}{19.4}[/tex]

[tex]x = 210[/tex]

There were 210 downloads of the standard version.

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