Question

a web music store offers two versions of a popular song. the size of the standard version is 2.3 megabytes (mb). the size of the high - quality version is 4.1 mb. yesterday, the high - quality version was downloaded three times as often as the standard version. the total size downloaded for the two versions was 4088 mb. how many downloads of the standard version were there?
number of standard version downloads:

Explanation:

Step1: Define variables for downloads

Let $x$ = number of standard version downloads.
Then $3x$ = number of high-quality downloads.

Step2: Set up total size equation

Total size = (size per standard × standard downloads) + (size per high-quality × high-quality downloads)
$$2.3x + 4.1(3x) = 4088$$

Step3: Simplify left-hand side

Calculate $4.1×3 = 12.3$, then combine terms:
$$2.3x + 12.3x = 4088$$
$$14.6x = 4088$$

Step4: Solve for $x$

Divide both sides by 14.6:
$$x = \frac{4088}{14.6}$$
$$x = 280$$

Answer:

280