Question

Andre wants to practice piano 9 hours a week. Each time he practices he practices for 2/3 hour. If he has already practiced 2 hours this week how many sessions,x, does he still need to practice to reach or surpass his goal?

Answer 1

Andre wants to practice a total of 9 hours in a week. He has already practiced for 2 hours, so we first need to calculate how many additional hours he needs to practice:

\[
9 \text{ hours} - 2 \text{ hours} = 7 \text{ hours}
\]

Now, each session he practices lasts for \(\frac{2}{3}\) hour. We need to determine how many sessions he needs to complete in order to reach his goal of 7 additional hours.

Let \( x \) be the number of sessions needed. The total time practiced in terms of \( x \) is:

\[
x \cdot \frac{2}{3} \text{ hour}
\]

We need this to be equal to or greater than 7 hours:

\[
x \cdot \frac{2}{3} \geq 7
\]

To solve for \( x \), we can multiply both sides of the inequality by \( \frac{3}{2} \):

\[
x \geq 7 \cdot \frac{3}{2}
\]

Calculating the right side:

\[
x \geq \frac{21}{2}
\]

\[
x \geq 10.5
\]

Since \( x \) must be a whole number (as he cannot have a fraction of a session), we round up to the nearest whole number:

\[
x \geq 11
\]

Thus, the number of sessions \( x \) that Andre still needs to practice to reach or surpass his goal is

\[
\boxed{11}
\]