Question

Bobby wants to practice his trumpet for at least 12 hours per week. He practices for three-fourths of an hour each session. If Bobby has already practiced for 3 hours this week, how many more sessions remain for him to meet or exceed his weekly practice goal?

If s represents the number of sessions, identify the correct inequality to represent this situation.

Answer 1

To determine how many more sessions Bobby needs to practice, we start with the following information:

1. Bobby wants to practice for at least 12 hours per week.
2. He has already practiced for 3 hours.
3. Each session lasts for three-fourths of an hour.

First, we need to find out how many hours Bobby still needs to practice to meet his goal.

The total hours he still needs is:
\[
12 \text{ hours} - 3 \text{ hours} = 9 \text{ hours}
\]

Next, we need to convert the hours he still needs into sessions. Each session is \(\frac{3}{4}\) of an hour. To find out how many sessions \(s\) he needs, we set up the equation based on the relationship between sessions and hours practiced:

Since each session lasts \(\frac{3}{4}\) of an hour, the total number of hours practiced in \(s\) sessions will be:
\[
\frac{3}{4}s
\]

We want this to be at least 9 hours to meet or exceed the remaining practice goal. Therefore, we set up the inequality:
\[
\frac{3}{4}s \geq 9
\]

To eliminate the fraction, we can multiply both sides of the inequality by 4:
\[
3s \geq 36
\]

Next, divide both sides by 3 to isolate \(s\):
\[
s \geq 12
\]

Thus, the correct inequality that represents the situation is:
\[
\frac{3}{4}s \geq 9
\]
And from solving it, we conclude that Bobby needs at least 12 more sessions to meet or exceed his weekly practice goal.