Need help solving a value mixture problem

Question

A Web music store offers two versions of a popular song. The size of the standard version is 2.5 megabytes (MB). The size of the high-quality version is 4.2 MB. Yesterday, there were 1050 downloads of the song, for a total download size of 2999 MB. How many downloads of the high-quality version were there? Needs to be solved using a linear equation.

Answer 1

X is the standard version

Y is the HQ version

 

X + Y = 1050

 

2.5X + 4.2Y = 2999

 

Solving the first equation for Y and multiplying the second equation by 10 to clear away the decimals:

 

Y = 1050 - X

 

25X + 42Y = 29990

 

25x + 42(1050 - x) = 29990

 

25x + 44100 - 42x = 29990

 

44100 - 17 x = 29990

 

 

-17x = -14110

 

x=830

 

y = 1050 - 830 = 220

 

CHECK : 830 x 2.5 +  220 * 4.2 = 2999

 

830 downloads of the standard version

and 220 of the enhanced, high-quality version