the standard version of a song is 2.3mb and high quality is 4.2mb. There was 1120 downloads for a total of 4077mb. How many high quality songs were downloaded?

Question

the standard version of a song is 2.3mb and high quality is 4.2mb. There was 1120 downloads for a total of 4077mb. How many high quality songs were downloaded?

Answer 1

As a retired computer professional (40+ years), a question about downloading mp3 files is “music to my ears” (pun intended).

Well, as you do with word problems, translate words into variables (use mnemonics = letters that remind you of their meaning and operations.

Let S equal the number of standard songs downloaded

H = number of high-quality songs downloaded

Given:  total number of downloads = 1120 = S + H

The size used by S standards songs is (2.3MB/song)*S   and the size used by H high-quality songs is (4.2MB/song)*H  and the total size is (given) 4077MB = (2.3MB)*S + (4.2MB)*H.

Mathematically, that means that we have two equations in two variables, so we can solve for both.  The question, however, asks for H, but we might also solve for S just to CHECK OUR ANSWER (important).

  4077 = 2.3 * (1120 – H) + 4.2 * H

  4077 =  2576 + 1.9*H

   H = 790

Checking:

   S = 1120 – 790 = 330   

     And

    2.3 * 330  + 4.2 * 790  does indeed take up 4077 MB of space

 

Answer 2

We assign variables for number of standard and number of high quality songs.

 

Let x = number of standard

Let y = number of HQ

 

 

Set up equation for total number of songs.

 

x + y = 1120              eq1

 

 

Set up equation for total number of mbs.

 

2.3x  4.2y = 4077            eq2

 

 

 

Lets substitute eq1 into eq2.  We can get eq2 in term of y since we want to know the number of HQ.

 

2.3(1120 - y) + 4.2y = 4077

 

 

Solve for y.