Aweb store offers two versions of a popular song. the size of the standard version is 2.5 megabytes. the size of the high-quality version is 4.6 megabytes. yesterday there were 1230 downloads of the song, for a total download size of 4797 megabytes. how many downloads of the standard version were there?

Define x and y :

Let x the number of 2.5M downloads.
Let y the number of 4.6M downloads.


Construct Equations :

There was a total of 1230 downloads.
⇒ x + y = 1230

Total downloaded size was 4797M.
⇒2.5x + 4.6y = 4797


Find x and y :

x + y = 1230 (1)
2.5x + 4.6y = 4797 (2)


From equation 1 :

x + y = 1230
x = 1230 - y                               // Take away y on both sides


Sub x = 1230 - y into equation 2 :

2.5 (1230 - y) + 4.6y = 4797      // Sub x = 1230 
3075 - 2.5y + 4.6y = 4797         // Apply distributive property
3075 + 2.1y = 4797                   // Combine like terms
2.1y = 1722                               // Take away 3075 from both sides
y = 820                                      // Divide by 2.1 on both sides


Sub y = 820 into equation 1 to find x :

x + y = 1230   
x + 820 = 1230                        // Sub y = 820
x = 410                                     // Take away 820 from both sides


Find the number of each type of downloads :

Number of 2.5M downloads = x = 410
Number of 4.6M downloads = y = 820 


There were 410 downloads for the standard version.

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