need help with math

Question

A Web music store offers two versions of a popular song. The size of the standard version is 2.7 megabytes (MB). The size of the high-quality version is 4.9 MB. Yesterday, the high-quality version was downloaded four times as often as the standard version. The total size downloaded for the two versions was 5798MB. How many downloads of the standard version were there?

Answer 1

"""

Variables starting with `hq` indicate

the 'high-quality' version. Variables starting

with `sv` indicate the 'standard version'.

"""

# Size of the two versions

hq_size = 4.9 # MB

sv_size = 2.7 # MB

total_size = 5798 # MB

"""

From the problem we know that `hq_downloads`

(the amount of downloads for the high quality version)

is equivalent to 4 times `sv_downloads` (the amount

of downloads for the standard version). We also know,

from the proble, that the total size downloaded for the

two versions was 5798 MB. Thus,

5798 MB = (hq_size * hq_downloads) + (sv_size * sv_downloads)

5798 MB = (4.9 MB * hq_downloads) + (2.7 MB * sv_downloads)

5798 MB = (4.9 MB * 4 * sv_downloads) + (2.7 MB * sv_downloads)

After replacing `hq_downloads` with 4*`sv_downloads`. We can solve

for `sv_downloads` in the expression above:

5798 MB = (4.9 MB * 4 * sv_downloads) + (2.7 MB * sv_downloads)

5798 MB = (19.6 MB * sv_downloads) + (2.7 MB * sv_downloads)

5798 MB = (19.6 MB + 2.7 MB) * sv_downloads

5798 MB = (22.3 MB) * sv_downloads

Therefore,

"""

sv_downloads = total_size / (hq_size * 4 + sv_size) # Dimensionless

print(f"There were {sv_downloads} downloads of the standard version.")

"""

The following should print upon running this code:

There were 260 downloads of the standard version.

"""