Question

Elena is trying to figure out how many movies she can download to her hard drive. The

hard drive is supposed to hold 500 gigabytes of data, but 58 gigabytes are already taken up
by other files. Each movie is 8 gigabytes. Elena wrote the inequality and
solved it to find the solution .

1. Explain how you know Elena made a mistake based on her solution.

2. Fix Elena’s inequality and explain what each part of the inequality means.

Answer 1

Answer: Elena used the "greater than" sign when she should have used the "less than sign".

The correct inequality is 8x + 58 < 500, where 8 is the amount of gigabytes taken up by a movie, x is the amount of movies, 58 is the amount of gigabytes already taken up, and 500 is the maximum storage capacity in gigabytes. The < sign denotes that 500 CANNOT be exceeded.

Explanation:

Elena wrote the equation as 8x + 58 > 500, meaning that the amount of gigabytes MUST exceed 500. This does not make sense since a computer would still function even with less movies. Since the hard drive has a capacity of 500 GB, it cannot go higher, making the correct inequality 8x + 58 < 500.