Word problem

Question

A web music store offers two versions of a popular song. the size of the standard version is 2.1 MB. The size of the high quality version is 4.5MB. Yesterday, the high quality version was downloaded three times as often as the standard version. the total size downloaded for the two versions was 3744 MB. How many downloads of the standard version were there?

Answer 1

x = number of downloads of the standard version

3x = number of downloads of the high quality version

 

(2.1 MB)(x) + (4.5MB)(3x) = 3744 MB

(2.1MB)(x) + (13.5MB)(x) = 3744 MB       associative law

(15.6MB)x = 3744MB                               distributive law

x = 3744MB/15.6MB                                 division

x = 240

Answer 2

Hello, 

 

First step is to convert the word problem into equations. Let H stand for High Quality downloads, and S be the standard quality downloads. 

 

From the paragraph, we know the entire amount of downloaded data is 3744. Therefore, we can write the following equation:

 

         (2.1 * S) + (4.5 * H) = 3744

 

We also know the the high quality (H) was downloaded 3 times as often as the standard version (S). In other words:

 

        3S = H

 

We can now take the second equation and plug it into the first, solving for S:

 

       2.1S +4.5*3S = 3744

     =2.1S + 13.5S = 3744

     =15.6S = 3744

     = 240 = S

 

Now, check the answer:

 

If S = 240, then H = 240* 3 = 720

 

720*4.5 + 240*2.1 = 3744