Question

You downloaded a video game to your computer. You have 60 minutes free trial of a game. It takes 5 1/6 minutes to set up the game and 7 1/3 minutes to play each lever. You want to find out how many levels you can play for free.

Which inequality describes the number of levels, l, you can play in 60 minutes?

Answer 1

First, we need to convert the mixed numbers to improper fractions to perform the calculations:

5 1/6 = (6 × 5 + 1) / 6 = 31 / 6

7 1/3 = (3 × 7 + 1) / 3 = 22 / 3

Let l be the number of levels we can play in 60 minutes. We have 60 minutes minus the time it takes to set up the game, which is 5 1/6 minutes, to give us the total playing time:

60 - 5 1/6 = 60 - 31/6 = 329/6

We can now set up an inequality to find the maximum number of levels we can play in this time:

l × 22/3 ≤ 329/6

Multiplying both sides by 3/22, we get:

l ≤ 329/6 × 3/22 = 47.545

Therefore, the inequality that describes the number of levels, l, we can play in 60 minutes is:

l ≤ 47.545

Since we can't play a fractional number of levels, we should round down to the nearest integer. Therefore, we can play a maximum of 47 levels for free within 60 minutes.