A web store offers two versions of a popular song. the size of the standard version is 2.5 megabytes. the size of the high-quali
ty 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
------------------------------------------------------------------------------------- Answer: There were 410 downloads for the standard version. -------------------------------------------------------------------------------------
