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. -------------------------------------------------------------------------------------
The answer to this question is that the trains will meet after 3 hours.
We can work this out by considering that is the closing speed of the two
trains is (50+60=)110 miles per hour, then this must mean that the
combined distance that the trains need to travel before they meet is 330
miles. If the time that is taken to travel 330 miles at 110 miles per
hour, then you simply need to divide 330/110 to find your answer - 3
hours.
