Math algebra word problem help

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=# of standard versions

let y=# of high-quality versions

x+y=920

2.8x+4.5y=3732

x+y=920

x=920-y

substitute

2.8(920-y)+4.5y=3732

2576-2.8y+4.5y=3732

2576+1.7y=3732

1.7y=3732-2576

1.7y=1156

17y=11,560

y=11,560/17

y=680 high-quality versions

x=920-680=240 standard versions

check: 240*2.8+680*4.5=672+3060=3732 MB