Question

Joseph received a $20 gift card for downloading music. Each downloaded song costs $1.29. Explain how to write and solve an inequality that can be used to determine the number of songs that he can purchase. Interpret the solution.

Answer 1

Let x be the number of songs downloaded.
Each song is $1.29; the total cost would be found by multiplying the cost by the number of songs, or 1.29x.
This cannot be more than 20, so we set this less than or equal to 20:
1.29x ≤ 20.

To solve this, we divide both sides by 1.29:
$\frac{1.29x}{1.29}$ ≤ $\frac{20}{1.29}$;
x ≤15.5.

We cannot download half of a song, so we round this down to 15 (although the number rounds up mathematically, he would not have enough money to download 16 songs). This means he can download at most 15 songs.

Answer 2

If x represents the number of downloads, you can write the inequality 1.29x = 20. Solving the inequality, you find that x is less than or equal to about 15.5. Since he can’t download part of a song, Joseph can download 15 or fewer songs.