word problem

Question

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 4.5 MB. Yesterday, there were 850 downloads of the song, for a total download size of 2799 MB. How many downloads of the standard version were there?

Answer 1

Let:

   S = number of standard versions

   H = number of high-quality versions

 

Note that:    (number of versions)*(MB per version) = MB       [for each type of song]

 

Translate:

   "850 downloads of the song"    means    S + H = 850      [eq1]

   "total download size of 2799 MB"    means    2.6S + 4.5H = 2799      [eq2]

   "How many downloads of the standard version were there?"  means   eliminate H; report S

 

Math:

    4.5S + 4.5H = 3825     [4.5*eq1]

    2.6S + 4.5H = 2799     [eq2 again]

  ---------------------------    [eliminate H by subtracting equations]

    1.9S            = 1026

         S           =   540       [divide both sides by 1.9]

 

The Standard Version of the song was downloaded 540 times.

Answer 2

Hello Natasha,

 

Let

S = # standard versions

H = # high quality versions

 

S + H = 850     Since there were 850 total downloads

2.6S + 4.5H = 2799  Since the total download was 2799 MB

 

-2.6S - 2.6H = -2210

2.6S + 4.5H = 2799

 

1.9H = 589

H = 310

 

S + 310 = 850

S = 540

 

There were 540 standard downloads.