Linear equation.

Question

A web music store offers two version of a popular song.the size of the standard version is 2.6 megabytes.the size of the high quality version is 4.1 megabytes. Yesterday the high quality version was downloaded twice as often as the standard version. The total size downloaded for the two versions was 3024 megabytes. How many downloads of the version were there?

Answer 1

First assign your variables

let x be the number of high quality version downloaded

let y be the number of standard version downloaded

next

translate the sentences to equations:

high quality version (x) was (=) downloaded twice (2 times) as often as the standard version (y)

x=2y this is your first equation

next translate this to equation as well

The total size downloaded for the two versions was 3024 megabytes.

remember standard version size: 2.6 megabytes

high quality version size: 4.1 megabytes

if x = the number of high quality version downloaded, and

y = the number of standard version downloaded

then

2.6 x + 4.1 y = 3024

from here you have two equations, and two variables

x = 2y

2.6 y + 4.1 x = 3024

2.6 y + 4.1 (2y) = 3024

2.6 y + 8.2 y = 3024

10.8 y = 3024

y = 280 (number of standard version downloaded)

x = 2y

x = 2(280)

x = 560 (number of high quality version downloaded)