Need help with this word problem being solved any way

Question

A Web music store offers two versions of a popular song. The size of the standard version is 2.8 megabytes (MB). The size of the high-quality version is 4.5 MB. Yesterday, there were 920 downloads of the song, for a total download size of 3732
MB. How many downloads of the standard version were there?

Answer 1

Hello, thank you for taking the time to post your question!

The key on this type of question is to set up a system of equations based on the given information. For this one we have

S + H = 920       since there were 920 total downloads of the song

2.8S + 4.5H = 3732     since the standard (S) has a size of 2.8, the high quality has a size of 4.5 and the total amount is 3732

I think the best way to solve is to substitute in H = 920 – S into the second equation and solve for S

When I do that I get S = 240, meaning that there were 240 downloads of the standard version.

I hope that helps get you moving in the right direction! Feel free to reach out if you have any additional questions beyond that :)

Answer 2

Let x = the number of 2.8 MB songs and y =  the number of 4.5 MB songs.

 

x + y = 920  and  2.8x + 4.5y = 3732

 

Solve the first equation for x, so  x = 920 - y. Now substitute in second equation.

 

2.8(920 - y) + 4.5y = 3732

 

distribute

 

2.8(920) - 2.8y + 4.5y = 3732

 

2576 + 1.7y = 3732

 

1.7y = 1156

 

y = 680  and  x = 240  i.e.  240 songs of 2.8 MB size   and    680 songs of 4.5 MB size

 

Thus 240 downloads of the standard version.