Question

Ilya puts a recording of a song up for sale online. He receives 80% of the profit from wach download of the song. The song is available for download at $1.29. How many downloads would he need to earn atleast $10,000? Convert to a algebraic equality and solve.

Answer 1

Answer:  7752

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Explanation:

x = number of songs downloaded, some positive whole number

1.29x = money earned from downloading those x songs

We want that expression to be at least $10,000. So we want 1.29x to be either equal to 10,000 or larger than it.

The inequality to set up is $1.29x \ge 10,000$

You can optionally erase the comma to get $1.29x \ge 10000$ though I think the comma helps it be more readable.

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To solve that inequality, we divide both sides by 1.29; this is to undo the multiplication of 1.29 to x.

$1.29x \ge 10,000\\\\1.29x/1.29 \ge 10,000/1.29\\\\x \ge 7,751.93798449612 \ \text{ .... approximate}\\\\x \ge 7,752$

We round up to the nearest whole number.

So there needs to be at least 7752 downloads for the profit to be $10,000 or more.