Word Problems

Question

A Web music store offers two versions of a popular song. The size of the standard version is 2.9 megabytes (MB). The size of the high-quality version is 4.6 MB. Yesterday, there were 1060 downloads of the song, for a total download size of 3431 MB. How many downloads of the high-quality version were there?

Answer 1

There are three helpful guidelines (best practices) to follow with this type of problem:
   - if possible, assign variables to the amount the problem asks you to find
   - correctly translate the words into concise, precise math expressions (with variables and operations)
   - be careful to use the correct units (and to convert then if necessary).

O.K. variables:   Let x = the number of downloads of the high-quality version

Then, translate:
   “there were 1060 downloads”    means
                          there were  1060-x  downloads of standard version
   “size of the standard version is 2.9 MB”   means     (2.9 MB * (1060-x))  of standard downloaded
   “size of the high-quality version is 4.6 MB”   means   (4.6 MB * x)  MB of h-q
   “total download size of 3431 MB”  means   add the two values above
   “How many downloads of the high-quality version were there?”    means      Report x

Now, the easy math:
   2.9(1060-x) + 4.6x = 3431
   29(1060-x) +46x = 34310    (multiply everything by 10 because I often forget decimals)
     -29x + 46x    = 34310 – 30740
       x    = 210

Checking (very important):
    Is    2.9(1060-210) + 4.6(210) = 3431    ?
         2465 + 966 = 3431   ?    yes!

Answer 2

Hi Jordyn,

 

So this kind of question calls for a multi-variable equation.  To solve we need two equations.  We can solve as follows:

 

2.9x+4.6y=3431

x+y=1060

Solve for x or y and then use that variable to solve for the other.  I hope this helps!